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Convergence rate for the incompressible limit of nonlinear diffusion-advection equations
Noemi David, Tomasz Dębiec, Benoît Perthame
The incompressible limit of nonlinear diffusion equations of porous medium type has attracted a lot of attention in recent years, due to its ability to link the weak formulation of…
A General Convex Integration Scheme for the Isentropic Compressible Euler Equations
Tomasz Dębiec, Jack W. D. Skipper, Emil Wiedemann
We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least ) to exact weak solution…
On entropy conservation for general systems of conservation laws
Tomasz Dębiec
In this work we consider companion conservation laws to general systems of conservation laws. We investigate sufficient regularity for weak solutions to satisfy companion laws, ass…
Energy Conservation for the Compressible Euler and Navier-Stokes Equations with Vacuum
Ibrokhimbek Akramov, Tomasz Dębiec, Jack W. D. Skipper +1
We consider the compressible isentropic Euler equations on with a pressure law , where . This includes all physically relevant…
Relative entropy method for measure-valued solutions in natural sciences
Tomasz Dębiec, Piotr Gwiazda, Kamila Łyczek +1
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the n…