On the evolution equation of compressible vortex sheets

 报告题目： On the evolution equation of compressible vortex sheets 报 告 人： Paolo Secchi教授（意大利布雷西亚大学） 报告时间： 2018年03月13日 16:00--17:00 报告地点： 理学院东北楼四楼报告厅（404） 报告摘要： We are concerned with supersonic vortex sheets for the Euler equations of compressible inviscid fluids in two space dimensions. For the problem with constant coefficients we derive an evolution equation for the discontinuity front of the vortex sheet. This is a pseudo-differential equation of order two. In agreement with the classical stability analysis, if the jump of the tangential component of the velocity satisfies $|[vcdottau]|<2sqrt {2},c$ (here $c$ denotes the sound speed) the symbol is elliptic and the problem is ill-posed. on the contrary, if $|[vcdottau]|>2sqrt{2},c$, then the problem is weakly stable, and we are able to derive a wave-type a priori energy estimate for the solution, with no loss of regularity with respect to the data. Then we prove the well-posedness of the problem, by showing the existence of the solution in weighted Sobolev spaces.