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Algebra i Analiz, 2020, Volume 32, Issue 1, Pages 121–186 (Mi aa1685)  

Research Papers

$L_2$-theory for two viscous fluids of different type: compressible and incompressible

V. A. Solonnikov

St. Petersburg Department of the Steklov Mathematical Institute, 27 Fontanka emb., 191023 St. Petersburg, Russia

Abstract: We prove the stability of 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.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00099_а


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Received: 02.02.2019
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Citation: V. A. Solonnikov, “$L_2$-theory for two viscous fluids of different type: compressible and incompressible”, Algebra i Analiz, 32:1 (2020), 121–186

Citation in format AMSBIB
\Bibitem{Sol20}
\by V.~A.~Solonnikov
\paper $L_2$-theory for two viscous fluids of different type: compressible and incompressible
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 1
\pages 121--186
\mathnet{http://mi.mathnet.ru/aa1685}


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