Related papers: $L^\infty$ solutions for a model of polytropic gas…
The paper proves existence of renormalized stationary solutions for a dense class of discrete velocity Boltzmann equations in the plane with given ingoing boundary values. The proof is based on the construction of a sequence of…
We prove the existence of global-in-time regular solutions to a system of stochastic quadratic reaction-diffusion equations. Global-in-time existence is based on a $L^\infty$-estimate obtained by an approach {\`a} la De Giorgi, as in…
The aim of this work is to propose a provably convergent finite volume scheme for the so-called Stefan-Maxwell model, which describes the evolution of the composition of a multi-component mixture and reads as a cross-diffusion system. The…
We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…
We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded domain $\Omega\subset\mathbb{R}^3$. Our first aim is to study…
The symmetries of the general Euler equations of fluid dynamics with polytropic exponent are determined using the Kaluza-Klein type framework of Duval et $\it{al}$. In the standard polytropic case the recent results of O'Raifeartaigh and…
In this paper, we are concerned with the Cauchy problem for isentropic gas dynamics. Through the contribution of many researchers such as Lax, P. D., Glimm, J., DiPerna, R. J. and Liu, T. P., the decay of solutions was established. They…
We introduce a family of mixed methods and discontinuous Galerkin discretisations designed to numerically solve the Oseen equations written in terms of velocity, vorticity, and Bernoulli pressure. The unique solvability of the continuous…
We consider self-similar potential flow for compressible gas with polytropic pressure law. Self-similar solutions arise as large-time asymptotes of general solutions, and as exact solutions of many important special cases like Mach…
We consider the model of viscous compressible multi-fluids with multiple velocities. We review different formulations of the model and the existence results for boundary value problems. We analyze crucial mathematical difficulties which…
The dynamics of multicomponent gas mixtures with vanishing barycentric velocity is described by Maxwell-Stefan equations with mass diffusion and heat conduction. The equations consist of the mass and energy balances, coupled to an algebraic…
The global existence of classical solutions to reaction-diffusion systems in dimensions one and two is proved. The considered systems are assumed to satisfy an {\it entropy inequality} and have nonlinearities with at most cubic growth in 1D…
In this paper, we prove the existence of classical solutions for the anisotropic surface diffusion with elasticity in the plane using a minimizing movements scheme, provided that the initial set is sufficiently regular. This scheme is…
A low diffusive flux difference splitting based kinetic scheme is developed based on a discrete velocity Boltzmann equation, with a novel three velocity model. While two discrete velocities are used for upwinding, the third discrete…
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…
This paper is concerned with one-dimensional 2 x 2 systems of conservation laws with a flux f=f(x, U) that is discontinuous with respect to the spatial variable. No monotonicity assumption is imposed on the mapping x \to f(x,U). We…
A method for deriving provably stable low-dimensional Galerkin models of post-transient incompressible flows is introduced. The proposed approach involves an iterative procedure for expansion modes that satisfy Lyapunov stability in the…
A broad conjecture, formulated by the authors in earlier work, reads as follows: "Cubic defocusing dispersive one dimensional flows with small initial data have global dispersive solutions". Notably, here smallness is only assumed in $H^s$…
We provide a natural simple argument using anistropic flows to prove the existence of weak solutions to Lutwak's $L^p$-Minkowski problem on $S^n$ which were obtained by other methods.
We are concerned with the existence and compactness of entropy solutions of the compressible Euler system for two-dimensional steady potential flow around an obstacle for a polytropic gas with supersonic far-field velocity. The existence…