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Home » Euler/Navier Stokes (Part 1): Global existence in the critical regularity setting for the compressible Navier-Stokes system in bounded domains

Seminar

Euler/Navier Stokes (Part 1): Global existence in the critical regularity setting for the compressible Navier-Stokes system in bounded domains February 11, 2021 (08:30 AM PST - 09:30 AM PST)
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Location: MSRI: Online/Virtual
Speaker(s) Raphaël Danchin (Université Paris-Est Créteil Val-de-Marne)
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To participate in this seminar, please register here: https://www.msri.org/seminars/25657

 

 

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To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract: We are concerned with the system satisfied by viscous compressible fluids in a bounded multi-dimensional

domain, in the case where the velocity vanishes at the boundary.  For perturbations of a stable constant equilibrium state with positive density, we prove global well-posedness in a critical regularity setting, thus extending classical results for the whole space. Our approach relies on (non standard) maximal regularity estimates for the linearization of the system, that follow from an abstract interpolation argument proposed by Da Prato and Grisvard in the seventies. We believe this approach to be useful for investigating more complex systems, including

free boundary problems. This is a joint work with Patrick Tolksdorf (Mainz University).

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