65 citations · 271 across the 31 of their papers we have counts for
36 papers
Global existence of weak solutions to a nematic electrolyte model in 2D
Hengrong Du, Fizay-Noah Lee, Gieri Simonett
In this paper, we study a system of partial differential equations modeling the dynamics of nematic electrolytes on a two-dimensional torus . The model couples the Po…
Global solutions for non-isothermal magnetoviscoelastic fluids in the absence of deformation diffusion
Yuanzhen Shao, Gieri Simonett
We study a non-isothermal model for incompressible magnetoviscoelastic fluids in , , coupling the incompressible Navier-Stokes equations with the evolution equ…
The primitive equations on curved surfaces
M. Hieber, Y. Shao, G. Simonett +1
In this paper, we study the primitive equations in a collar neighborhood of a smooth closed hypersurface in . Using the framework of maximal -regularity and the…
On nematic electrolytes
Hengrong Du, Fizay-Noah Lee, Gieri Simonett
We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nemati…
Coriolis-driven fluid motion on spherical surfaces
Yuanzhen Shao, Gieri Simonett, Mathias Wilke
We consider the motion of an incompressible viscous fluid on a sphere, incorporating the effects of the Coriolis force. We demonstrate that global solutions exist for any divergenc…
The Navier-Stokes equations on manifolds with boundary
Yuanzhen Shao, Gieri Simonett, Mathias Wilke
We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes e…
On a thermodynamically consistent model for magnetoviscoelastic fluids in 3D
Hengrong Du, Yuanzhen Shao, Gieri Simonett
We introduce a system of equations that models a non-isothermal magnetoviscoelastic fluid. We show that the model is thermodynamically consistent, and that the critical points of t…
Well-posedness for magnetoviscoelastic fluids in 3D
Hengrong Du, Yuanzhen Shao, Gieri Simonett
We show that the system of equations describing a magnetoviscoelastic fluid in three dimensions can be cast as a quasilinear parabolic system. Using the theory of maximal -reg…
-calculus for the surface Stokes operator and applications
Gieri Simonett, Mathias Wilke
We consider a smooth, compact and embedded hypersurface without boundary and show that the corresponding (shifted) surface Stokes operator admits a bounded $H^\inft…
On the Navier-Stokes equations on surfaces
Jan Pruess, Gieri Simonett, Mathias Wilke
We consider the motion of an incompressible viscous fluid that completely covers a smooth, compact and embedded hypersurface without boundary and flows along . Local-in-time…
On the motion of a fluid-filled rigid body with Navier Boundary conditions
Giusy Mazzone, Jan Pruess, Gieri Simonett
We consider the inertial motion of a system constituted by a rigid body with an interior cavity entirely filled with a viscous incompressible fluid. Navier boundary conditions are…
A maximal regularity approach to the study of motion of a rigid body with a fluid-filled cavity
Giusy Mazzone, Jan Pruess, Gieri Simonett
We consider the inertial motion of a rigid body with an interior cavity that is completely filled with a viscous incompressible fluid. The equilibria of the system are characterize…
On the microscopic bidomain problem with FitzHugh-Nagumo ionic transport
Jan Pruess, Gieri Simonett
The microscopic bidomain problem with FitzHhugh-Nagumo ionic transport is studied in the -framework. Reformulating the problem as a semilinear evolution equation on th…
The Rayleigh-Taylor instability for the Verigin problem with and without phase transition
Jan Pruess, Gieri Simonett, Mathias Wilke
Isothermal compressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy's law for the velocity field. It is…
Critical spaces for quasilinear parabolic evolution equations and applications
Jan Pruess, Gieri Simonett, Mathias Wilke
We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal -regularity in time-wei…
On the Muskat flow
Jan Pruess, Gieri Simonett
Of concern is the motion of two fluids separated by a free interface in a porous medium, where the velocities are given by Darcy's law. We consider the case with and without phase…
The Verigin problem with and without phase transition
Jan Pruess, Gieri Simonett
Isothermal compressible two-phase flows with and without phase transition are modeled, employing Darcy's and/or Forchheimer's law for the velocity field. It is shown that the resul…
Stability of equilibrium shapes in some free boundary problems involving fluids
Gieri Simonett, Mathias Wilke
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2)…
Well-posedness and long-time behavior for the Westervelt equation with absorbing boundary conditions of order zero
Gieri Simonett, Mathias Wilke
We investigate the Westervelt equation from nonlinear acoustics, subject to nonlinear absorbing boundary conditions of order zero, which were recently proposed by Kaltenbacher & Sh…
On the flow of non-axisymmetric perturbations of cylinders via surface diffusion
Jeremy LeCrone, Gieri Simonett
We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders in . Using tools from parabolic theo…
On the regularity of the interface of a thermodynamically consistent two-phase Stefan problem with surface tension
Jan Pruess, Yuanzhen Shao, Gieri Simonett
We study the regularity of the free boundary arising in a thermodynamically consistent two-phase Stefan problem with surface tension by means of a family of parameter-dependent dif…
Some Remarks on Uniformly Regular Riemannian Manifolds
Marcelo Disconzi, Yuanzhen Shao, Gieri Simonett
We establish the equivalence between the family of closed uniformly regular Riemannian manifolds and the class of complete manifolds with bounded geometry.
On incompressible two-phase flows with phase transitions and variable surface tension
Jan Pruess, Senjo Shimizu, Gieri Simonett +1
Our study of the basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics [10,11,12,16] is extended to the case of temperature-dependent…
Continuous maximal regularity on uniformly regular Riemannian manifolds
Yuanzhen Shao, Gieri Simonett
We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show tha…