Siberian Advances in Mathematics

, Volume 28, Issue 4, pp 233–264 | Cite as

Mathematical Theory of Fluids in Motion

  • E. Feireisl


The goal of this paper is to present the recent development of mathematical fluid dynamics in the framework of classical continuum mechanics phenomenological models. In particular, we discuss the Navier–Stokes (viscous) and the Euler (inviscid) systems modeling the motion of a compressible fluid. The theory is developed from fundamental physical principles, the necessary mathematical tools introduced at the moment when needed. In particular, we discuss various concepts of solutions and their relevance in applications. Particular interest is devoted to well-posedness of the initial-value problems and their approximations including possibly certain numerical schemes.


Navier–Stokes–Fourier system mathematical fluid dynamics weak solution. 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPrahaCzech Republic

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