Heterogeneities in fluid mechanics

Pressure law which depends on the density and on time and space variables $t$ and $x$ for compressible flows or anelastic constraint on the velocity field in the incompressible setting for the rate of flow are examples of heterogeneities that may complicate mathematical analysis in the weak regularity context. I will explain different mathematical difficulties occuring in such situations and new developments recently obtained in collaboration with P.-E. Jabin and F. Wang.

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