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Sib. Èlektron. Mat. Izv., 2009, Volume 6, Pages 120–165 (Mi semr59)  

This article is cited in 2 scientific papers (total in 2 papers)

Research papers

Global solvability of the multidimensional equations of compressible non-Newtonian fluids, transport equation and the Orlicz spaces

A. E. Mamontov

M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: The article illustrates the application of the theory of the Orlicz spaces in global solvability of boundary value problems for the equations of multidimensional flows of viscous compressible fluids and for the transport equation. While solving the main problem, a new method of extrapolation from the scale of the Lebesgue spaces into the Orlicz spaces is developed basing on integral representations and transforms of $N$-functions. The efficiency of the extrapolation method developed here is illustrated by the uniqueness problem for the Euler equations. A wide review of known results is given wherever necessary.

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Document Type: Article
UDC: 517.95, 517.51
MSC: 76N10, 35F10, 44A35, 46E30
Received May 19, 2009, published June 4, 2009

Citation: A. E. Mamontov, “Global solvability of the multidimensional equations of compressible non-Newtonian fluids, transport equation and the Orlicz spaces”, Sib. Èlektron. Mat. Izv., 6 (2009), 120–165

Citation in format AMSBIB
\Bibitem{Mam09}
\by A.~E.~Mamontov
\paper Global solvability of the multidimensional equations of compressible non-Newtonian fluids, transport equation and the Orlicz spaces
\jour Sib. \`Elektron. Mat. Izv.
\yr 2009
\vol 6
\pages 120--165
\mathnet{http://mi.mathnet.ru/semr59}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2586682}
\elib{http://elibrary.ru/item.asp?id=13035579}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Guo Sh., Tan Zh., “Large-Time Behaviour of Solutions to a Class of Non-Newtonian Compressible Fluids”, NoDea-Nonlinear Differ. Equ. Appl., 24:3 (2017), 23  crossref  mathscinet  zmath  isi  scopus
    2. Barrett J.W., Lu Y., Suli E., “Existence of Large-Data Finite-Energy Global Weak Solutions to a Compressible Oldroyd-B Model”, Commun. Math. Sci., 15:5 (2017), 1265–1323  crossref  mathscinet  zmath  isi  scopus
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