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Algebra i Analiz, 2020, Volume 32, Issue 1, Pages 121–186 (Mi aa1685)  
This article is cited in 4 scientific papers (total in 5 papers)

Research Papers

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

V. A. Solonnikov

St. Petersburg Department of the Steklov Mathematical Institute, 27 Fontanka emb., 191023 St. Petersburg, Russia
Full-text PDF (545 kB) Citations (5)
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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-Slobodetskiĭspaces $ 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
Supported in part by RFBR grant no. 17-01-00099
Received: 02.02.2019
English version:
St. Petersburg Mathematical Journal, 2021, Volume 32, Issue 1, Pages 91–137
DOI: https://doi.org/10.1090/spmj/1640
Bibliographic databases:
Document Type: Article
MSC: 76N10
Language: English
Citation: V. A. Solonnikov, “$ L_2$-theory for two viscous fluids of different types: Compressible and incompressible”, Algebra i Analiz, 32:1 (2020), 121–186; St. Petersburg Math. J., 32:1 (2021), 91–137
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и анализ St. Petersburg Mathematical Journal
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