# LORENTZ SPACES IN ACTION ON PRESSURELESS SYSTEMS ARISING FROM MODELS OF COLLECTIVE BEHAVIOR RAPHAËL DANCHIN, PIOTR BOGUSLAW MUCHA AND PATRICK TOLKSDORF

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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Preprints, Working Papers, ...

Cited literature [40 references]

https://hal-upec-upem.archives-ouvertes.fr/hal-02568285
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Submitted on : Monday, November 2, 2020 - 7:20:10 PM
Last modification on : Tuesday, September 28, 2021 - 5:16:27 PM

### Files

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### Identifiers

• HAL Id : hal-02568285, version 2
• ARXIV : 2005.05603

### Citation

Raphaël Danchin, Piotr Bogusław Mucha, Patrick Tolksdorf. LORENTZ SPACES IN ACTION ON PRESSURELESS SYSTEMS ARISING FROM MODELS OF COLLECTIVE BEHAVIOR RAPHAËL DANCHIN, PIOTR BOGUSLAW MUCHA AND PATRICK TOLKSDORF. 2020. ⟨hal-02568285v2⟩

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