$ L_2$-theory for two viscous fluids of different types: Compressible and incompressible

V. A. Solonnikov

Algebra i analiz, Tome 32 (2020) no. 1, pp. 121-186.

Résumé

Stability is proved for the rest state in the problem of evolution of two viscous fluids, compressible and incompressible, contained in a bounded vessel and separated by a free interface. The fluids are subject to mass and capillary forces. The proof of stability is based on “maximal regularity” estimates for the solution in the anisotropic Sobolev-Slobodetskiĭspaces $ W_2^{r,r/2}$ with an exponential weight.

Détail

Keywords: free boundaries, compressible and incompressible fluids, Sobolev–Slobodetskiĭ spaces.

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