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Analysis of a Compressible Navier-Stokes System with Dispersive Effects
- Speaker(s)
- Michał Trelka
- Affiliation
- MIM UW
- Language of the talk
- English
- Date
- Jan. 22, 2026, 12:30 p.m.
- Room
- room 5070
- Seminar
- Seminar of Mathematical Physics Equations Group
We cordially invite you for the talk:
We consider a compressible Navier-Stokes system with additional dispersive effects induced by rotation through a Coriolis-type term. Such a model arises naturally in geophysical fluid dynamics, in magnetohydrodynamics, and in the theory of complex fluids, where rotation or internal structure produces anisotropy and oscillatory dynamics. The equations combine hyperbolic acoustic waves, parabolic viscous dissipation and dispersive rotational effects, leading to a delicate multiscale behavior.
The analysis is carried out in critical Besov spaces, which are naturally adapted to the parabolic and dispersive structure of the system. This choice is motivated by the behavior of the heat equation: its smoothing effect is accurately captured in Besov norms but cannot be fully exploited in Sobolev spaces at the critical level. Moreover, the critical Besov space forms a Banach algebra, allowing a robust control of the nonlinear transport and coupling terms.
We present a well-posedness approach using Strichartz-type estimates combined with a fixed point argument to construct solutions in the critical Besov framework.
