# Analysis Seminar

#### Finite Energy Method for Compressible Fluids

**Speaker:**
Philippe LeFloch, University of Paris 6

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, September 20, 2012, 11 a.m.

**Synopsis:**

I will discuss the initial value problem for the Euler system of compressible fluid flows governed by a general pressure law, when solutions enjoy a certain symmetry (for instance, plane symmetry) and have solely finite total energy. In a recent series of papers with Pierre Germain (Courant Institute), I have established an existence and compactness theory for this problem and analyzed the vanishing viscosity--capillarity limit in weak solutions with finite energy to the Navier-Stokes-Korteweg system. The proposed approach is referred to as the Finite Energy Method for compressible fluid flows and leads to a generalization of DiPerna's theorem (bounded solutions) and LeFloch-Westdickenberg's theorem (finite energy solutions) to the Euler system of polytropic fluids.