Abstract.
We introduce the main known results of the theory of incompressible and compressible vortex sheets. Moreover, we present recent results obtained by the author with J. F. Coulombel about supersonic compressible vortex sheets in two space dimensions. The problem is a nonlinear free boundary hyperbolic problem with two difficulties: the free boundary is characteristic and the Lopatinski condition holds only in a weak sense, yielding losses of derivatives. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the boundary value problem obtained by linearization around an unsteady piecewise solution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Secchi, P. On Compressible Vortex Sheets. J. math. fluid mech. 7 (Suppl 2), S254–S272 (2005). https://doi.org/10.1007/s00021-005-0158-6
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s00021-005-0158-6