Local existence for the linearized compressible Euler
equation with a free boundary
Uwe Brauer∗ and Gabriel Nagy†
∗ Departamento
† Gabriel
de Matemática Aplicada, Universidad Complutense, Madrid
Nagy Department of Mathematics, Michigan State University
Abstract
An initial free-boundary problem for the compressible Euler equation is considered, in order to describe the time evolution of a body with a sharp boundary. Our
approach is as follows. First, we transform the free–boundary problem into a fixedboundary problem in the usual way by using the Lagrange formulation of Euler’s
equations. We then write the resulting system as a first order system of evolution
and constraint equations. We then apply known results for initial fixed-boundary
value problem using maximal dissipative boundary conditions. The treatment of the
constraints at the boundary turns out to be the most difficult part of our approach.
1