Gieri Simonett
Professor
Department of Mathematics
Vanderbilt University
Nashville, TN 37240
Office: Stevenson Center 1524
Phone: (615) 322-6658 or 322-6672
Email: gieri.simonett "at" vanderbilt.edu
Google Scholar
Research Interests
-
Nonlinear Partial Differential Equations
- Free Boundary Problems
- Fluid Dynamics
- Phase Transitions
- Geometric Evolution Equations
- Theory of Function Spaces
Books
Jan Prüss, Gieri Simonett,
Moving Interfaces and Quasilinear Parabolic Evolution Equations.
Monographs in Mathematics, vol. 105,
Birkhäuser, 2016.
Moving Interfaces
In this monograph, the authors develop a comprehensive approach for the mathematical
analysis of a wide array of problems involving moving interfaces.
The approach includes an in-depth study of abstract quasilinear parabolic evolution equations,
elliptic and parabolic boundary value problems, transmission problems,
one- and two-phase Stokes problems, and the equations of incompressible viscous
one- and two-phase fluid flows.
An essential ingredient is the theory of maximal regularity, which is fully developed.
The authors present a modern approach based on powerful tools in classical analysis,
functional analysis, and vector-valued harmonic analysis.
The theory is applied to problems in two-phase fluid dynamics and phase transitions,
one-phase generalized Newtonian fluids, nematic liquid crystal flows,
Maxwell-Stefan diffusion, and a variety of geometric evolution equations.
In addition, the monograph contains a discussion of the underlying physical
and thermodynamic principles governing the equations of fluid flows and phase transitions,
and an exposition of the geometry of moving hypersurfaces.
Edited Volumes
Mathematical Models in Medical and Health Science.
Papers from the International Conference held at
Vanderbilt University,
Nashville, TN, May 28-31, 1997.
Edited by Mary Ann Horn, Gieri Simonett and Glenn F. Webb.
Innovations in Applied Mathematics. Vanderbilt University Press,
Nashville, TN, 1998.
www.vanderbilt.edu/vupress
Topics in Nonlinear Analysis. The Herbert Amann Anniversary Volume.
Edited by Joachim Escher and Gieri Simonett.
Progress in Nonlinear Differential Equations and their
Applications, Vol. 35.
Birkhäuser Verlag, Basel, 1999.
Nonlinear Analysis
Parabolic Problems.
The Herbert Amann Festschrift.
Edited by
J. Escher, P. Guidotti, M. Hieber, P. Mucha, J. Prüss,
Y. Shibata, G. Simonett, C. Walker and W. Zajaczkowski.
Progress in Nonlinear Differential Equations and Their Applications, Vol. 80.
Springer Basel, 2011.
Parabolic Problems
Special Issue Nonlinear parabolic problems and applications.
Edited by P. Guidotti, G. Simonett.
Discrete and Continuous Dynamical Systems.
Vol 26, Number 2, 2010.
Special Issue: Parabolic Evolution Equations, Maximal Regularity, and Applications.
Dedicated to Jan Jan Prüss.
Edited by
D. Bothe, R. Denk, M. Hieber, R. Schnaubelt, G. Simonett, M. Wilke, R. Zacher.
Journal of Evolution Equations 17 (2017), no. 1.
Special Issue: Evolution Equations - New Perspectives for Theory and Applications.
Dedicated to Matthias Hieber.
Edited by
R. Denk, Y. Giga, H. Kozono, J. Saal, G. Simonett, E. Titi.
Journal of Evolution Equations 21 (2017), no. 3.
Co-organizer of Conferences and Workshops (since 2015)
2015 Shanks Workshop on Mathematical Aspects of Fluid Dynamics.
Vanderbilt University, February 28-March 1, 2015.
Fluid Dynamics
International Conference on Evolution Equations
in conjunction with the 31st annual Shanks Lecture.
With a special tribute to the work of Jan Prüss
on the occasion of his 65th birthday.
Vanderbilt University, May 16-20, 2016.
Evolution Equations
2017 Shanks Workshop on Mathematical Aspects of Fluid Dynamics.
Vanderbilt University, April 8-9, 2017.
Fluid Dynamics
2018 Shanks Workshop on Mathematical Aspects of Fluid Dynamics.
Vanderbilt University, March 24-25, 2018.
Fluid Dynamics
Conference Maximal Regularity and Nonlinear PDE.
Research Institute for Mathematical Sciences, University of Kyoto, March 26-30, 2019.
Kyoto
International Conference Nonlinear Analysis in Honour of Herbert Amann´s 80th Birthday.
Cortona, Italy, June 11-14, 2019.
Cortona
2020 Shanks Workshop on Mathematical Aspects of Fluid Dynamics,.
Vanderbilt University, March 14-15, 2020.
Cancelled.
Fluid Dynamics
2022 Shanks Workshop on Mathematical Aspects of Fluid Dynamics,.
Vanderbilt University, February 19-20, 2022.
Fluid Dynamics
Selected Publications
Herbert Amann, Matthias Hieber, Gieri Simonett,
Bounded $H_\infty$-calculus for elliptic operators.
Differential Integral Equations 7 (1994), 613-653.
(pdf file).
Gieri Simonett,
Invariant manifolds and bifurcation for quasilinear reaction-diffusion systems.
Nonlinear Anal. 23 (1994), 515-544.
(pdf file).
Gieri Simonett,
Center manifolds for quasilinear reaction-diffusion systems.
Differential Integral Equations 8
(1995), no. 4, 753-796.
(pdf file).
Joachim Escher, Gieri Simonett
Maximal regularity for a free boundary problem.
NoDEA Nonlinear Differential Equations Appl. 2
(1995), no. 4, 463-510.
(pdf file).
Joachim Escher, Gieri Simonett
Analyticity of the interface in a free boundary problem.
Math. Ann. 305
(1996), no. 3, 439-459.
(pdf file).
Joachim Escher, Gieri Simonett,
On Hele-Shaw models with surface tension.
Math. Res. Lett. 3 (1996), no. 4,
467-474.
(pdf file).
Xuan T. Duong, Gieri Simonett,
$H_\infty$-calculus for elliptic operators with non-smooth coefficients.
Differential Integral Equations 10
(1997), 201-217.
(pdf file).
Joachim Escher, Gieri Simonett,
Classical solutions of multi-dimensional Hele-Shaw models.
SIAM J. Math. Anal. 28 (1997), 1028-1047.
(pdf file).
Joachim Escher, Gieri Simonett,
Classical solutions for Hele-Shaw models with surface tension.
Adv. Differential Equations 2 (1997),
619-642.
(pdf file).
Joachim Escher, Gieri Simonett
Classical solutions for the quasi-stationary Stefan problem
with surface tension.
Differential Equations, Asymptotic
Analysis, and Mathematical Physics
(M. Demuth and B.-W. Schulze,
eds.),
Mathematical Research Vol. 100, Akademie Verlag, Berlin (1997),
619-642.
(pdf file).
Joachim Escher, Gieri Simonett,
A center manifold analysis for the Mullins-Sekerka model.
J. Differential Equations 143
(1998), 267-292.
(pdf
file).
Joachim Escher, Gieri Simonett,
The volume preserving mean curvature flow near spheres.
Proc. Amer. Math. Soc. 126
(1998), 2789-2796.
(pdf file).
Joachim Escher, Uwe Mayer, Gieri Simonett,
The surface diffusion flow for immersed hypersurfaces.
SIAM J. Math. Anal. 29
(1998), 1419-1433.
(pdf file).
Joachim Escher, Uwe Mayer, Gieri Simonett,
On the surface diffusion flow.
Proc. Intern. Conf. on Navier-Stokes Equations
and Related Problems,
TEV/VSP, Vilnius/Utrecht (1998), 69-80.
(pdf or
ps file).
Joachim Escher, G. Simonett,
Moving surfaces and abstract parabolic evolution equations.
Topics in Nonlinear Analysis. The Herbert Amann
Anniversary Volume,
Birkhäuser, Basel (1999), 183-212.
(pdf or
ps file).
Uwe Mayer, Gieri Simonett,
Classical solutions for diffusion-induced grain-boundary motion.
Journal Math. Anal. Appl.
234 (1999), 660-674.
(pdf file).
Uwe Mayer, Gieri Simonett,
On diffusion-induced grain-boundary motion.
Nonlinear Partial Differential Equations
(G.Q. Chen and E. DiBenedetto, eds.),
Contemporary Mathematics 238,
AMS, Providence (1999), 231-240.
(pdf file).
Uwe Mayer, Gieri Simonett,
Self-intersections for the surface diffusion
and the the
volume preserving mean curvature flow.
Differential Integral Equations
13 (2000), 1189-1199.
(pdf file).
G. Simonett,
The Willmore flow near spheres.
Differential Integral Equations
14 (2001), 1005-1014.
(pdf or
ps file).
Philippe Clement, Gieri Simonett,
Maximal regularity in continuous interpolation spaces
and quasilinear parabolic equations.
J. Evolution Equations
1 (2001), 39-67.
(pdf file).
Uwe F. Mayer, Gieri Simonett,
A numerical scheme for axisymmetric solutions
of curvature driven
free boundary problems,
with applications to the Willmore flow.
Interfaces and Free Boundaries
4 (2002), 1-22.
(pdf or
ps file).
Numerical simulations
Uwe F. Mayer, Gieri Simonett,
Self-intersections for the Willmore flow.
Evolution Equations: Applications to Physics, Industry, Life Sciences
and Economics.
EVEQ 2000 Conference in Levico Terme (Trento, Italy).
Birkhauser, Basel (2003), 341-348.
(pdf or
ps file).
Joachim Escher, Jan Prüss, Gieri Simonett,
A new approach to the regularity of solutions for
parabolic equations.
Evolution Equations,
Lecture Notes in Pure and Appl. Math., 234, Dekker, New York, 2003, 167-190.
(pdf file).
Joachim Escher, Jan Prüss, Gieri Simonett,
Analytic solutions for a Stefan problem with
Gibbs-Thomson correction.
J. Reine Angew. Math. 563
(2003), 1-52.
(pdf file).
Joachim Escher, Gieri Simonett,
Analyticity of solutions to fully nonlinear
parabolic evolution equations
on symmetric spaces.
J. Evolution Equations 3
(2003), 549-576.
(pdf file).
Philippe Clement, Stig-Olof Londen, Gieri Simonett,
Quasilinear evolutionary equations and continuous
interpolation spaces.
J. Differential Equations 196
(2004), 418-447.
(pdf file).
Jan Prüss, Gieri Simonett,
Maximal regularity for evolution equations in weighted L_p spaces.
Arch. Math. 82 (2004), 415-431.
(pdf file).
Dieter Bothe, Jan Prüss, Gieri Simonett,
Well-posedness of a two-phase flow with soluble surfactant.
In: Nonlinear Elliptic and Parabolic Problems. A Special Tribute to the Work of
Herbert Amann.
Progress in Nonlinear Differential Equations and Their Applications, Vol. 64,
Birkhäuser, Basel, 2005, 37-62.
(pdf file).
Gieri Simonett, Christoph Walker,
On the solvability of a mathematical model for prion proliferation.
J. Math. Anal. Appl. 324 (2006), 580-603.
(pdf file).
Jan Prüss, Gieri Simonett,
Operator-valued symbols for elliptic and
parabolic problems on wedges.
Partial Differential Equations and Functional Analysis.
Operator Theory: Advances and Applications, Vol. 168,
Birkhäuser, Basel (2006), 189-208.
(pdf file).
Jan Prüss, Gieri Simonett,
$H^\infty$-calculus for the sum of non-commuting operators.
Trans. Amer. Math. Soc. 359 (2007), 3549-3565.
(pdf file).
Jan Prüss, Jürgen Saal, Gieri Simonett,
Existence of analytic solutions for
the classical Stefan problem.
Math. Ann. 338 (2007), 703-755.
(pdf file).
Jan Prüss, Jürgen Saal, Gieri Simonett,
Analytic solutions for the classical two-phase Stefan problem.
Proceedings of Equadiff-11, (2007), 415-425.
(pdf file).
Jan Prüss, Gieri Simonett,
Maximal regularity for degenerate evolution equations with an exponential
weight function.
Functional Analysis and Evolution Equations. Dedicated to Gunter Lumer.
Birkhäuser, Basel (2007), 531-546.
(pdf file).
Jan Prüss, Gieri Simonett,
Stability of equilibria for the Stefan problem with surface tension.
SIAM J. Math. Anal. 40 (2008), 675-698.
(pdf file).
Jan Prüss, Gieri Simonett, Rico Zacher,
On convergence of solutions to equilibria for quasilinear parabolic problems.
J. Differential Equations 246 (2009), 3902-3931.
(pdf file).
Jan Prüss, Gieri Simonett, Rico Zacher,
On normal stability for nonlinear parabolic equations.
Discrete Contin. Dyn. Syst. 2009,
Dynamical Systems, Differential Equations and Applications.
7th AIMS Conference, suppl.,
612-621.
(pdf file).
Jan Prüss, Gieri Simonett,
Analysis of the boundary symbol for the two-phase Navier-Stokes equations
with surface tension.
Banach Center Publ. 86 (2009), 265-285.
(pdf file)
Jan Prüss, Gieri Simonett,
On the two-phase Navier-Stokes equations with surface tension.
Interfaces Free Bound. 10 (2010), 311-345.
( pdf file).
Jan Prüss, Gieri Simonett,
Analytic solutions for the two-phase Navier-Stokes equations with
surface tension and gravity.
In: Parabolic Problems. The Herbert Amann Festschrift.
Progress in Nonlinear Differential Equations and Their Applications, Vol. 80,
Birkhäuser, Basel (2011), 507-540.
math arXiv
Jan Prüss, Gieri Simonett,
On the Rayleigh-Taylor instability for the two-phase Navier-Stokes equations
with surface tension.
Indiana Univ. Math. J. 59 (2010), 1853-1872.
(pdf file).
Jeremy LeCrone, Gieri Simonett,
Continuous maximal regularity and analytic semigroups.
Discrete Contin. Dyn. Syst. 2011, Dynamical Systems, Differential Equations and Applications.
8th AIMS Conference. Suppl. Vol. II, 963-970.
math arXiv
Jan Prüss, Senjo Shimizu, Yoshihiro Shibata, Gieri Simonett,
On well-posedness of incompressible two-phase flows with phase transitions: the case of equal densities.
Evolution Equations and Control Theory 1 (2012), 171-194.
(pdf file).
Jan Prüss, Gieri Simonett, Rico Zacher,
Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension.
Arch. Ration. Mech. Anal. 207 (2013), 611-667.
(pdf file).
Jan Prüss, Gieri Simonett, Mathias Wilke,
Invariant foliations near normally hyperbolic equilibria for quasilinear parabolic problems.
Advanced Nonlinear Studies 13 (2013), 231-243.
math arXiv
Jan Prüss, Gieri Simonett,
On the manifold of closed hypersurfaces in Rn.
Discrete Contin. Dyn. Syst. 33 (2013), 5407-5428.
(pdf file).
Jan Prüss, Jürgen Saal, Gieri Simonett,
Singular limits for the two-phase Stefan problem.
Discrete Contin. Dyn. Syst. 33 (2013), 5379-5405.
(pdf file).
Jeremy LeCrone, Gieri Simonett,
On well-posedness, stability, and bifurcation for the axisymmetric surface diffusion flow.
SIAM J. Math. Anal. 45 (2013), no. 5, 2834-2869.
(pdf file).
Jan Prüss, Gieri Simonett, Rico Zacher,
On the qualitative behavior of incompressible two-phase flows with phase transitions: the case of equal densities.
Interfaces Free Bound. 15 (2013), 405-428.
(pdf file).
Yuanzhen Shao, Gieri Simonett,
Continuous maximal regularity on uniformly regular Riemannian manifolds.
J. Evol. Equ. 14 (2014), 211-248.
(pdf file).
Jan Prüss, Yuanzhen Shao, Gieri Simonett,
On the regularity of the interface of a thermodynamically consistent
two-phase Stefan problem with surface tension.
Interfaces Free Bound. 17 (2015), 555-600.
math arXiv
Jan Prüss, Senjo Shimizu, Gieri Simonett, Mathias Wilke,
On incompressible two-phase flows with phase transitions and variable surface tension.
In: Recent Developments of Mathematical Fluid Mechanics.
Advances in Mathematical Fluid Mechanics, Birkhäuser/Springer, Basel (2016), 411-442.
math arXiv
Marcelo Disconzi, Yuanzhen Shao, Gieri Simonett,
Some remarks on uniformly regular Riemannian manifolds.
Math. Nachr. 289 (2016), 232-242.
DOI 10.1002/mana.201400354.
math arXiv
Jan Prüss, Gieri Simonett, Mathias Wilke,
On thermodynamically consistent Stefan problems with variable surface energy.
Arch. Ration. Mech. Anal. 220 (2016), 603-638.
DOI 10.1007/s00205-015-0938-y.
math arXiv
Jeremy LeCrone, Gieri Simonett,
On the flow of non-axisymmetric perturbations of cylinders via surface diffusion.
J. Differential Equations 260 (2016), 5510-5531.
math arXiv
Jan Prüss, Gieri Simonett,
On the Muskat flow.
Evolution Equations and Control Theory 5 (2016), 631-645.
math arXiv
Gieri Simonett, Mathias Wilke,
Well-posedness and long-time behavior for the Westervelt equation
with absorbing boundary conditions of order zero.
J. Evolution Equations 7 (2017), 511-571.
math arXiv
Jan Prüss, Gieri Simonett, Mathias Wilke,
Critical spaces for quasilinear parabolic evolution equations and applications.
J. Differential Equations 264 (2018), 2028-2074.
math arXiv
Jan Prüss, Gieri Simonett,
The Verigin problem with and without phase transition.
Interfaces Free Bound. 20 (2018), 107-128.
math arXiv
Gieri Simonett, Mathias Wilke,
Stability of equilibrium shapes in some free boundary problems involving fluids.
Handbook of mathematical analysis in mechanics of viscous fluids, 1221–1265, Springer, 2018.
math arXiv
Jan Prüss, Gieri Simonett, Mathias Wilke,
The Rayleigh-Taylor instability for the Verigin problem with and without surface tension.
NoDEA Nonlinear Differential Equations Appl. 26 (2019), no. 3, Art. 18, 35 pp.
math arXiv
Giusy Mazzone, Jan Prüss, Gieri Simonett,
A maximal regularity approach to the study of motion of a rigid body with a fluid-filled cavity.
J. Math. Fluid Mech. 21 (2019), no. 3, Art. 44, 20 pp.
math arXiv
Giusy Mazzone, Jan Prüss, Gieri Simonett,
On the motion of a fluid-filled rigid body with Navier boundary conditions.
SIAM J. Math. Anal. 51 (2019), 1582-1606.
math arXiv
Jan Prüss, Gieri Simonett,
On the microscopic bidomain problem with FitzHugh-Nagumo ionic transport.
J. Elliptic and Parabolic Equations 5 (2019), 25–45.
math arXiv
Jeremy LeCrone, Gieri Simonett,
On quasilinear parabolic equations and continuous maximal regularity.
Evolution Equations and Control Theory 9 (2020), 61–86.
math arXiv
Jeremy LeCrone, Yuanzhen Shao, Gieri Simonett,
The surface diffusion and the Willmore flow for uniformly regular hypersurfaces.
Discrete Contin. Dyn. Syst. Ser. S 13 (2020), 3503-3524.
math arXiv
Jan Prüss, Gieri Simonett, Mathias Wilke,
On the Navier-Stokes equations on surfaces.
J. Evolution Equations 21 (2021), 3153-3179.
math arXiv
Gieri Simonett, Mathias Wilke,
H∞-calculus for the surface Stokes operator and applications.
Submitted.
math arXiv
Hengrong Du, Yuanzhen Shao, Gieri Simonett,
Well-posedness for magnetoviscoelastic fluids in 3D.
Submitted.
math arXiv