Related papers: $\mathcal{A}$-free rigidity and applications to th…
We design an energy-stable and asymptotic-preserving finite volume scheme for the compressible Euler system. Using the relative energy framework, we establish rigorous error estimates that yield convergence of the numerical solutions in two…
We consider a modified Euler equation on $\mathbb R^2$. We prove existence of weak global solutions for bounded (and fast decreasing at infinity) initial conditions and construct Gibbs-type measures on function spaces which are…
In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…
We study the limiting behavior of the solutions of Euler equations of one-dimensional compressible fluid flow as the pressure like term vanishes. This system can be thought of as an approximation for the one dimensional model for large…
Recently developed concept of dissipative measure-valued solution for compressible flows is a suitable tool to describe oscillations and singularities possibly developed in solutions of multidimensional Euler equations. In this paper we…
We consider the Cauchy problem for a semilinear stochastic differential inclusion in a Hilbert space. The linear operator generates a strongly continuous semigroup and the nonlinear term is multivalued and satisfies a condition which is…
We consider several modifications of the Euler system of fluid dynamics including its pressureless variant driven by non-local interaction repulsive-attractive and alignment forces in the space dimension $N=2,3$. These models arise in the…
We prove the existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic…
We prove the weak-strong uniqueness for measure-valued solutions of the incompressible Euler equations. These were introduced by R.DiPerna and A.Majda, and in particular global existence to any L2 initial data was proven. Whether…
Two fundamental models in plasma physics are given by the Vlasov-Maxwell-Boltzmann system and the compressible Euler-Maxwell system which both capture the complex dynamics of plasmas under the self-consistent electromagnetic interactions at…
We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of H\"older regularity $C^{1/2}$, valued in $C^0_{t, loc} L^2_x$ endowed with the strong topology. The…
In this paper, we consider the helicity conservation of weak solutions for the compressible Euler equations in a bounded domain with general pressure law and vacuum. We deduce a sufficient condition for a weak solution conserving the…
In this paper, we consider the compressible Euler-Maxwell equations arising in semiconductor physics, which take the form of Euler equations for the conservation laws of mass density and current density for electrons, coupled to Maxwell's…
We propose a spectral viscosity method (SVM) to approximate the incompressible Euler equations driven by a multiplicative noise. We show that SVM solution converges to a dissipative measure-valued martingale solution. These solutions are…
We give a new sufficient criteria to prove the uniqueness of the incompressible Euler equation in dimension $N\geq2$. In their celebrated works by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\'ekelyhidi Jr. [7] they have…
Euler alignment systems appear as hydrodynamic limits of interacting self-propelled particle systems such as the (generalized) Cucker-Smale model. In this work, we study weak solutions to an Euler alignment system on smooth, bounded,…
The Euler-$\alpha$ equations model the averaged motion of an ideal incompressible fluid when filtering over spatial scales smaller than $\alpha$. We show that there exists $\beta>1$ such that weak solutions to the two and three dimensional…
This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic…
We derive an explicit formula for global weak solutions of the one dimensional system of pressure-less Euler-Poisson equations. Our variational formulation is an extension of the well-known formula for entropy solutions of the scalar…
In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued -- strong uniqueness principle. This means that they coincide with a strong solution…