×

Rectilinear vortex sheets of inviscid liquid-gas two-phase flow: linear stability. (English) Zbl 1334.35253

Summary: The vortex sheet solutions are considered for the inviscid liquid-gas two-phase flow. In particular, the linear stability of rectilinear vortex sheets in two spatial dimensions is established for both constant and variable coefficients. The linearized problem of vortex sheet solutions with constant coefficients is studied by means of Fourier analysis, normal mode analysis, and Kreiss symmetrizer, while the linear stability with variable coefficients is obtained by Bony-Meyer paradifferential calculus theory. The linear stability is crucial to the existence of vortex sheet solutions of the nonlinear problem. A novel symmetrization and some weighted Sobolev norms are introduced to study the hyperbolic linearized problem with characteristic boundary.

MSC:

35Q35 PDEs in connection with fluid mechanics
35L50 Initial-boundary value problems for first-order hyperbolic systems
35L65 Hyperbolic conservation laws
76T10 Liquid-gas two-phase flows, bubbly flows
PDFBibTeX XMLCite
Full Text: DOI