The stability of compressible vortex sheets in two space dimensions Jean-Francois CoulombelPaolo Secchi 76N1035Q3535L5076E17vortex sheetscompressible fluidsstabilitysymmetrizersenergy estimates We study the linear stability of compressible vortex sheets in two space dimensions. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the linearized boundary value problem. Since the problem is characteristic, the estimate we prove exhibits a loss of control on the trace of the solution. Furthermore, the failure of the uniform Kreiss-Lopatinskii condition yields a loss of derivatives in the energy estimate. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2526 10.1512/iumj.2004.53.2526 en Indiana Univ. Math. J. 53 (2004) 941 - 1012 state-of-the-art mathematics http://iumj.org/access/