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arXiv · 2005.05603

Lorentz spaces in action on pressureless systems arising from models of collective behavior

Raphaël Danchin·Piotr Boguslaw Mucha·Patrick Tolksdorf
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Abstract

We are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $L_{q,r}(0,T;L_p(\Omega))$ spaces.

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Raphaël Danchin, Piotr Boguslaw Mucha, Patrick Tolksdorf. 2020-05-12. Lorentz spaces in action on pressureless systems arising from models of collective behavior. https://arxiv.org/abs/2005.05603

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