𝐿₂-theory for two viscous fluids of different types: Compressible and incompressible

Solonnikov, V.

doi:10.1090/spmj/1640

$L_2$-theory for two viscous fluids of different types: Compressible and incompressible
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by V. A. Solonnikov

St. Petersburg Math. J. 32 (2021), 91-137

DOI: https://doi.org/10.1090/spmj/1640

Published electronically: January 11, 2021

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Abstract:

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–Slobodetskiĭ spaces $W_2^{r,r/2}$ with an exponential weight.

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