4 citations · 12 across the 11 of their papers we have counts for
9 papers · 1 filter
Gradient and Hessian regularity in elliptic transmission problems near a point cusp
Dieter Bothe, Pierre-Etienne Druet, Robert Haller
We consider elliptic transmission problems in several space dimensions near an interface which is diffeomorphic to an axisymmetric reference-interface with a singular poi…
A regularity result for quasilinear elliptic systems with an equation of energy-type
Pierre-Etienne Druet
We study the continuity of weak solutions for quasilinear elliptic systems with source terms of critical growth arising from a transport-energy structure. The latter occurs frequen…
Hyperbolic-parabolic normal form and local classical solutions for cross-diffusion systems with incomplete diffusion
Pierre-Étienne Druet, Katharina Hopf, Ansgar Jüngel
We investigate degenerate cross-diffusion equations with a rank-deficient diffusion matrix that are considered to model populations which move as to avoid spatial crowding and have…
Incompressible limit for a fluid mixture
Pierre-Etienne Druet
In this paper we discuss the incompressible limit for multicomponent fluids in the isothermal ideal case. Both a direct limit-passage in the equation of state and the low Mach-numb…
Maximal mixed parabolic-hyperbolic regularity for the full equations of multicomponent fluid dynamics
Pierre-Etienne Druet
We consider a Navier-Stokes-Fick-Onsager-Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the result…
Well-posedness analysis of multicomponent incompressible flow models
Dieter Bothe, Pierre-Etienne Druet
In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as the independence…
A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion
Pierre-Etienne Druet
After the pioneering work by Giovangigli on mathematics of multicomponent flows, several attempts were made to introduce global weak solutions for the PDEs describing the dynamics…
Mass transport in multicomponent compressible fluids: Local and global well-posedness in classes of strong solutions for general class-one models
Dieter Bothe, Pierre-Etienne Druet
We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Ma…
Analysis of cross-diffusion systems for fluid mixtures driven by a pressure gradient
Pierre-Etienne Druet, Ansgar Jüngel
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pres…