Global existence of weak solutions to viscoelastic phase separation: part II. Degenerate case

Existence of Global Weak Solutions for 3d Degenerate Compressible Navier-stokes Equations

In this paper, we prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosity. The method is based on the Bresch and Desjardins entropy conservation [2]. The main contribution of this paper is to derive the Mellet-Vasseur type inequality [32] for the weak solutions, even if it is not verified by the first level of approximation. This provid...

Global existence of weak solutions to some micro - macro models

We prove global existence of weak solutions for the co-rotational FENE dumbbell model and the Doi model also called the Rod model. The proof is based on propagation of compactness, namely if we take a sequence of weak solutions which converges weakly and such that the initial data converges strongly then the weak limit is also a solution. To cite this article: A. Name1, A. Name2, C. R. Acad. Sc...

Existence of Weak Solutions to a Class of Degenerate Semiconductor Equations Modeling Avalanche Generation

Global Existence of Weak Solutions for the Burgers-Hilbert Equation

This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L(IR). For positive times, the solution lies in L2∩L∞. A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.

Global Existence of Weak Solutions for a Viscous Two-phase Model

The purpose of this paper is to explore a viscous two-phase liquid-gas model relevant for well and pipe flow. Our approach relies on applying suitable modifications of techniques previously used for studying the single-phase isothermal Navier-Stokes equations. A main issue is the introduction of a novel two-phase variant of the potential energy function needed for obtaining fundamental a priori...