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Izv. Akad. Nauk SSSR Ser. Mat., 1987, Volume 51, Issue 5, Pages 1065–1087 (Mi izv1331)  

This article is cited in 19 scientific papers (total in 19 papers)

On the transient motion of an isolated volume of viscous incompressible fluid

V. A. Solonnikov


Abstract: Solvability locally in time is proved for a free-boundary problem describing the evolution of a finite mass of viscous incompressible fluid in $\mathbf R^n$, $n=2,3$, without taking surface tension into account. Sufficient conditions for the extension of a solution to the infinite time interval $t>0$ are given. A solution is obtained in the space $W_p^{2,1}$ with $p>n$.
Bibliography: 19 titles.

Full text: PDF file (2364 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1988, 31:2, 381–405

Bibliographic databases:

UDC: 517.944.4
MSC: 35Q10, 76D05
Received: 27.06.1986

Citation: V. A. Solonnikov, “On the transient motion of an isolated volume of viscous incompressible fluid”, Izv. Akad. Nauk SSSR Ser. Mat., 51:5 (1987), 1065–1087; Math. USSR-Izv., 31:2 (1988), 381–405

Citation in format AMSBIB
\Bibitem{Sol87}
\by V.~A.~Solonnikov
\paper On~the transient motion of an isolated volume of viscous incompressible fluid
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1987
\vol 51
\issue 5
\pages 1065--1087
\mathnet{http://mi.mathnet.ru/izv1331}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=925094}
\zmath{https://zbmath.org/?q=an:0850.76180}
\transl
\jour Math. USSR-Izv.
\yr 1988
\vol 31
\issue 2
\pages 381--405
\crossref{https://doi.org/10.1070/IM1988v031n02ABEH001081}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yoshikazu Giga, Shuji Takahashi, “On Global Weak Solutions of the Nonstationary Two-Phase Stokes Flow”, SIAM J Math Anal, 25:3 (1994), 876  crossref  mathscinet  zmath  isi
    2. Atusi Tani, Naoto Tanaka, “Large-time existence of surface waves in incompressible viscous fluids with or without surface tension”, Arch Rational Mech Anal, 130:4 (1995), 303  crossref  mathscinet  zmath  adsnasa
    3. I Ciuperca, “A Navier–Stokes problem with free boundary”, Applied Mathematics Letters, 9:5 (1996), 39  crossref  elib
    4. C GRANDMONT, Y MADAY, “Existence de solutions d'un problème de couplage fluide-structure bidimensionnel instationnaire”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:4 (1998), 525  crossref
    5. Céline Grandmont, Yvon Maday, “Existence for an Unsteady Fluid-Structure Interaction Problem”, ESAIM: M2AN, 34:3 (2002), 609  crossref
    6. Alexandre Caboussat, “Numerical simulation of two-phase free surface flows”, Arch Computat Methods Eng, 12:2 (2005), 165  crossref
    7. Helmut Abels, “Generalized Stokes resolvent equations in an infinite layer with mixed boundary conditions”, Math Nachr, 279:4 (2006), 351  crossref  mathscinet  zmath  isi
    8. J. Math. Sci. (N. Y.), 152:5 (2008), 625–637  mathnet  crossref  elib
    9. Yoshihiro Shibata, Senjo Shimizu, “On the L<sub>p</sub>-L<sub>q</sub> maximal regularity of the Neumann problem for the Stokes equations in a bounded domain”, crll, 2008:615 (2008), 157  crossref  mathscinet  zmath  isi
    10. Raphaël Danchin, Piotr Bogusław Mucha, “A critical functional framework for the inhomogeneous Navier–Stokes equations in the half-space”, Journal of Functional Analysis, 256:3 (2009), 881  crossref
    11. Giovanna Guidoboni, Marcello Guidorzi, Mariarosaria Padula, “Continuous Dependence on Initial Data in Fluid–Structure Motions”, J math fluid mech, 2010  crossref
    12. Hantaek Bae, “Solvability of the free boundary value problem of the Navier–Stokes equations”, DCDS-A, 29:3 (2010), 769  crossref
    13. Ryôhei Kakizawa, “Maximal Lp-Lq regularity of the linearized initial–boundary value problem for motion of compressible viscous fluids”, Journal of Differential Equations, 2011  crossref
    14. Chongsheng Cao, Ciprian G Gal, “Global solutions for the 2D NS–CH model for a two-phase flow of viscous, incompressible fluids with mixed partial viscosity and mobility”, Nonlinearity, 25:11 (2012), 3211  crossref
    15. Manuel Nesensohn, “Generalized Viscoelastic Fluids with a Free Boundary without Surface Tension”, SIAM J. Math. Anal, 46:1 (2014), 428  crossref
    16. V. A. Solonnikov, “L p -Theory of the Problem of Motion of Two Incompressible Capillary Fluids in a Container”, J Math Sci, 2014  crossref
    17. I.V.lad. Denisova, “On Energy Inequality for the Problem on the Evolution of Two Fluids of Different Types Without Surface Tension”, J. Math. Fluid Mech, 2015  crossref
    18. Yoshihiro Shibata, “On some free boundary problem of the Navier–Stokes equations in the maximal <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>–<mml:math altimg="si2.gif" overflow="scroll"”, Journal of Differential Equations, 2015  crossref
    19. Karen Yeressian, “On Varifold Solutions of Two-Phase Incompressible Viscous Flow with Surface Tension”, J. Math. Fluid Mech, 2015  crossref
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