65 citations · 166 across the 21 of their papers we have counts for
27 papers
-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…
Well-Posedness and Qualitative Behaviour of a Two-phase Navier-Stokes/Mullins-Sekerka system with boundary contact
Maximilian Rauchecker, Mathias Wilke
We consider a coupled two-phase Navier-Stokes/Mullins-Sekerka system describing the motion of two immiscible, incompressible fluids inside a bounded container. The moving interface…
Well-Posedness and qualitative behaviour of the Mullins-Sekerka problem with ninety-degree angle boundary contact
Helmut Abels, Maximilian Rauchecker, Mathias Wilke
We show local well-posedness for the Mullins-Sekerka system with ninety degree angle boundary contact. We will describe the motion of the moving interface by a height function over…
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…