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Limite incompressible de solutions du système d’Euler compressible 2-D dans certains cas mal préparés

Alexandre Dutrifoy (2002/2003)

Séminaire Équations aux dérivées partielles

Les effets dispersifs permettent de passer à la limite dans le système d’Euler compressible 2-D isentropique, quand le nombre de Mach tend vers zéro, même si les données initiales ne sont pas uniformément régulières.Ceci mène à des résultats de convergence vers des solutions non régulières du système d’Euler incompressible, comme les poches de tourbillon ou les solutions de Yudovich.

Local-in-time existence for the non-resistive incompressible magneto-micropolar fluids

Peixin Zhang, Mingxuan Zhu (2022)

Applications of Mathematics

We establish the local-in-time existence of a solution to the non-resistive magneto-micropolar fluids with the initial data u 0 H s - 1 + ε , w 0 H s - 1 and b 0 H s for s > 3 2 and any 0 < ε < 1 . The initial regularity of the micro-rotational velocity w is weaker than velocity of the fluid u .

Low-Mach consistency of a class of linearly implicit schemes for the compressible Euler equations

Kučera, Václav, Lukáčová-Medviďová, Mária, Noelle, Sebastian, Schütz, Jochen (2021)

Programs and Algorithms of Numerical Mathematics

In this note, we give an overview of the authors’ paper [6] which deals with asymptotic consistency of a class of linearly implicit schemes for the compressible Euler equations. This class is based on a linearization of the nonlinear fluxes at a reference state and includes the scheme of Feistauer and Kučera [3] as well as the class of RS-IMEX schemes [8,5,1] as special cases. We prove that the linearization gives an asymptotically consistent solution in the low-Mach limit under the assumption of...

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