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Zapiski Nauchnykh Seminarov POMI, 2020, Volume 489, Pages 96–112 (Mi znsl6926)  
Local solvability of free boundary problem for viscous compressible and incompressible fluids in the spaces $W_p^{2+l,1+l/2}(Q_T)$, $p>2$

V. A. Solonnikov

С.-Петербургское отделение Математического института им. В. А. Стеклова РАН, Фонтанка 27, 191023 Санкт-Петербург, Россия
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Abstract: We prove local in time solvability of the free boundary problem for two phase viscous compressible and incompressible fluids in the spaces $W_p^{2+l,1+l/2}(Q_T)$ with $p>2$, $l\in(1/p,2/p)$.
Key words and phrases: $L_p$-estimates, free boundary problems, local solvability.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00397
The research was partially supported by RFBR grant No. 20-01-00397.
Received: 12.12.2019
Document Type: Article
UDC: 517
Language: English
Citation: V. A. Solonnikov, “Local solvability of free boundary problem for viscous compressible and incompressible fluids in the spaces $W_p^{2+l,1+l/2}(Q_T)$, $p>2$”, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Zap. Nauchn. Sem. POMI, 489, POMI, St. Petersburg, 2020, 96–112
Citation in format AMSBIB
\Bibitem{Sol20}
\by V.~A.~Solonnikov
\paper Local solvability of free boundary problem for viscous compressible and incompressible fluids in the spaces $W_p^{2+l,1+l/2}(Q_T)$, $p>2$
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~48
\serial Zap. Nauchn. Sem. POMI
\yr 2020
\vol 489
\pages 96--112
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6926}
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