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 Wr,r/22 with an exponential weight.
Keywords:
free boundaries, compressible and incompressible fluids, Sobolev–Slobodetskiĭ spaces.
Citation:
V. A. Solonnikov, “L2-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
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\by V.~A.~Solonnikov
\paper $ L_2$-theory for two viscous fluids of different types: Compressible and incompressible
\jour Algebra i Analiz
\yr 2020
\vol 32
\issue 1
\pages 121--186
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\transl
\jour St. Petersburg Math. J.
\yr 2021
\vol 32
\issue 1
\pages 91--137
\crossref{https://doi.org/10.1090/spmj/1640}
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Linking options:
https://www.mathnet.ru/eng/aa1685
https://www.mathnet.ru/eng/aa/v32/i1/p121
This publication is cited in the following 5 articles:
I. V. Denisova, “Suschestvovanie figur ravnovesiya vraschayuscheisya kapillyarnoi dvukhfaznoi zhidkosti”, Algebra i analiz, 36:3 (2024), 62–80
V. A. Solonnikov, M. A. Vivaldi, “Evolution free boundary problem for the Navier–Stokes equations”, Algebra i analiz, 36:3 (2024), 213–238
G. I. Bizhanova, I. V. Denisova, A. I. Nazarov, K. I. Pileckas, V. V. Pukhnachev, S. I. Repin, J.-F. Rodrigues, G. A. Seregin, N. N. Uraltseva, E. V. Frolova, “On the 90th birthday of Vsevolod Alekseevich Solonnikov”, Russian Math. Surveys, 78:5 (2023), 971–981
V. A. Solonnikov, “Local Solvability of Free Boundary Problem for Viscous Compressible and Incompressible Fluids in the Spaces $ {W}_p^{2+l,1+l/2} $ (QT), p > 2”, J Math Sci, 260:1 (2022), 63
Citation in format AMSBIB
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