50 citations · 111 across the 15 of their papers we have counts for
17 papers
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…
On critical spaces for the Navier-Stokes equations
Jan Pruess, Mathias Wilke
The abstract theory of critical spaces developed in [22] and [20] is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip co…
Addendum to the Paper "On Quasilinear Parabolic Evolution Equations in Weighted -Spaces II"
Jan Pruess, Mathias Wilke
This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper [6]. The improvement is explained in Section 1 and proved in Section 2. The importance…
Dynamics of the Ericksen-Leslie Equations with General Leslie Stress I: The Incompressible Isotropic Case
Matthias Hieber, Jan Prüss
The Ericksen-Leslie model for nematic liquid crystals in a bounded domain with general Leslie and isotropic Ericksen stress is studied in the case of a non-isothermal and incompres…
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…
On quasilinear parabolic evolution equations in weighted Lp-spaces II
Jeremy LeCrone, Jan Pruess, Mathias Wilke
Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low…
Reaction-diffusion systems of Maxwell-Stefan type with reversible mass-action kinetics
Martin Herberg, Martin Meyries, Jan Prüss +1
The mass-based Maxwell-Stefan approach to one-phase multicomponent reactive mixtures is mathematically analyzed. It is shown that the resulting quasilinear, strongly coupled reacti…
Singular limits for the two-phase Stefan problem
Jan Pruess, Juergen Saal, Gieri Simonett
We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinatio…
On a Class of Energy Preserving Boundary Conditions for Incompressible Newtonian Flows
Dieter Bothe, Matthias Köhne, Jan Prüss
We derive a class of energy preserving boundary conditions for incompressible Newtonian flows and prove local-in-time well-posedness of the resulting initial boundary value problem…
On thermodynamically consistent Stefan problems with variable surface energy
Jan Pruess, Gieri Simonett, Mathias Wilke
A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these probl…
Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
Jan Pruess, Gieri Simonett, Rico Zacher
The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these…
Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes Equations with Surface Tension
Matthias Köhne, Jan Pruess, Mathias Wilke
The two-phase free boundary value problem for the isothermal Navier-Stokes system is studied for general bounded geometries in absence of phase transitions, external forces and bou…
On conserved Penrose-Fife type models
Jan Pruess, Mathias Wilke
In this paper we investigate quasilinear parabolic systems of conserved Penrose-Fife type. We show maximal - regularity for this problem with inhomogeneous boundary data. Fur…
On quasilinear parabolic evolution equations in weighted -spaces
Matthias Köhne, Jan Pruess, Mathias Wilke
In this paper we develop a geometric theory for quasilinear parabolic problems in weighted -spaces. We prove existence and uniqueness of solutions as well as the continuous de…
On the Rayleigh-Taylor Instability for the two-Phase Navier-Stokes Equations
Jan Pruess, Gieri Simonett
The two-phase free boundary problem with surface tension and downforce gravity for the Navier-Stokes system is considered in a situation where the initial interface is close to equ…
Analytic solutions for the two-phase Navier-Stokes equations with surface tension and gravity
Jan Pruess, Gieri Simonett
We consider the motion of two superposed immiscible, viscous, incompressible, capillary fluids that are separated by a sharp interface which needs to be determined as part of the p…
On normal stability for nonlinear parabolic equations
Jan Pruess, Gieri Simonett, Rico Zacher
We show convergence of solutions to equilibria for quasilinear and fully nonlinear parabolic evolution equations in situations where the set of equilibria is non-discrete, but form…