65 citations · 114 across the 8 of their papers we have counts for
10 papers · 1 filter
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…
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…
Rayleigh-Taylor instability for the two-phase Navier-Stokes equations with surface tension in cylindrical domains
Mathias Wilke
This article is concerned with the dynamic behaviour of two immiscible and incompressible fluids in a cylindrical domain, which are separated by a sharp interface. In case that the…
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…