Ruan, Lizhi; Wang, Dehua; Weng, Shangkun; Zhu, Changjiang Rectilinear vortex sheets of inviscid liquid-gas two-phase flow: linear stability. (English) Zbl 1334.35253 Commun. Math. Sci. 14, No. 3, 735-776 (2016). 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. Cited in 15 Documents 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 Keywords:inviscid liquid-gas two-phase flow; vortex sheet; linear stability PDFBibTeX XMLCite \textit{L. Ruan} et al., Commun. Math. Sci. 14, No. 3, 735--776 (2016; Zbl 1334.35253) Full Text: DOI