Related papers: A General Convex Integration Scheme for the Isentr…
In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-valued solutions of the compressible Euler equations converge…
In this paper, we introduce a decomposition lemma that allows error terms to be expressed using fewer rank-one symmetric matrices than $\frac{n(n+1)}{2}$ within the convex integration scheme of constructing flexible $C^{1,\alpha}$ solutions…
We propose a spectral viscosity method to approximate the two-dimensional Euler equations with rough initial data and prove that the method converges to a weak solution for a large class of initial data, including when the initial vorticity…
A new type of systematic approach to study the incompressible Euler equations numerically via the vanishing viscosity limit is proposed in this work. We show the new strategy is unconditionally stable that the $L^2$-energy dissipates and…
In this paper, the design and analysis of a class of second order accurate IMEX finite volume schemes for the compressible Euler equations in the zero Mach number limit is presented. In order to account for the fast and slow waves, the…
We present an extension to high-order of a first-order Lagrange-projection like method for the approximation of the Euler equations introduced in Coquel {\it et al.} (Math. Comput., 79 (2010), pp.~1493--1533). The method is based on a…
In this paper, a novel fully-explicit weakly compressible solver is developed for solving incompressible two-phase flows. The two-phase flow is modelled by coupling the general pressure equation, momentum conservation equations and the…
A class of differentiable solutions is proved for the isentropic Euler equations in two and three space dimensions. The solutions are explicitly given in terms of solutions to inviscid Burgers equations, and several directions of…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
We consider two models of a compressible inviscid isentropic two-fluid flow. The first one describes the liquid-gas two-phase flow. The second one can describe the mixture of two fluids of different densities or the mixture of fluid and…
This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of…
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 complete Euler system describing the time evolution of an inviscid non-isothermal gas. We show that the rarefaction wave solutions of the 1D Riemann problem are stable, in particular unique, in the class of all bounded weak…
We show that for any $\gamma < \frac{1}{3}$ there exist H\"{o}lder continuous weak solutions $v \in C^{\gamma}([0,T] \times \mathbb{T}^2)$ of the two-dimensional incompressible Euler equations that strictly dissipate the total kinetic…
New exact solutions are obtained for several nonlinear physical equations, namely the Navier-Stokes and Euler systems, an isentropic compressible fluid system and a vector nonlinear Schroedinger equation. The solution methods make use of…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded…
We give sufficient conditions on the regularity of solutions to the inhomogeneous incompressible Euler and the compressible isentropic Euler systems in order for the energy to be conserved. Our strategy relies on commutator estimates…
In this work we study the asymptotic behavior of solutions of the incompressible two-dimensional Euler equations in the exterior of a single smooth obstacle when the obstacle becomes very thin tending to a curve. We extend results by…
Recently the second and third author developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in H\"older spaces (arXiv:1202.1751 and arXiv:1205.3626 (2012)). The motivation comes from Onsager's…