Isentropic Fluid Dynamics in a Curved Pipe

In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow in an arbitrarily curved, piecewise smooth pipe. We consider initial data in the subsonic regime, with small total variation about a stationary solution. The proof relies on the front-tracking method and is based on [1]

Entropy functions for symmetric systems of conservation laws

It is shown that symmetric systems of conservation laws are equipped with a one-parameter family of entropy functions. A simple symmetrizability criterion is used

Isometric Immersions via Compensated Compactness for Slowly Decaying Negative Gauss Curvature and Rough Data

In this paper the method of compensated compactness is applied to the problem of isometric immersion of a two dimensional Riemannian manifold with negative Gauss curvature into three dimensional Euclidean space. Previous applications of the method to this problem have required decay of order $t^{-4}$ in the Gauss curvature. Here we show that the decay of Hong $t^{-2-\delta/2}$ where $\delta\in(0,4)$ suffices

An overview of some recent results on the Euler system of isentropic gas dynamics

In this overview we discuss some recent results of non--uniqueness for the isentropic Euler equations of gas dynamics with particular attention to the role of some admissibility criteria proposed in the literature.Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1312.471

Low Mach number limit for the Quantum-Hydrodynamics system

In this paper we deal with the low Mach number limit for the system of quantum-hydrodynamics, far from the vortex nucleation regime. More precisely, in the framework of a periodic domain and ill-prepared initial data we prove strong convergence of the solutions towards regular solutions of the incompressible Euler system. In particular we will perform a detailed analysis of the time oscillations and of the relative entropy functional related to the system.Comment: To appear in Research in the Mathematical Science