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Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems

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Abstract

A rigorous justification of several well-known mathematical models of incompressible fluid flows can be given in terms of singular limits of the scaled Navier-Stokes-Fourier system, where some of the characteristic numbers become small or large enough. We discuss the problem in the framework of global-in-time solutions for both the primitive and the target system.

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  1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

  2. Basque Center for Applied Mathematics, Parque Technológico de Bizkaia 500, Derio, Spain

    Eduard Feireisl

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  1. Eduard Feireisl
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Lecture held in the Seminario Matematico e Fisico on September 21, 2009.

The work of E.F. was supported by Grant 201/08/0315 of GA ČR as a part of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503. The paper was written during author’s stay at BCAM (Basque Center for Applied Mathematics) in Bilbao, which hospitality and support are gladly acknowledged.

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Feireisl, E. Mathematical Models of Incompressible Fluids as Singular Limits of Complete Fluid Systems. Milan J. Math. 78, 523–560 (2010). https://doi.org/10.1007/s00032-010-0128-1

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