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# Communications in Mathematical Sciences

## Volume 14 (2016)

### Number 3

### Rectilinear vortex sheets of inviscid liquid-gas two-phase flow: Linear stability

Pages: 735 – 776

DOI: http://dx.doi.org/10.4310/CMS.2016.v14.n3.a7

#### Authors

#### Abstract

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.

#### Keywords

inviscid liquid-gas two-phase flow, vortex sheet, linear stability

#### 2010 Mathematics Subject Classification

34B05, 35L50, 35L65, 76T10

Published 26 February 2016