LORENTZ SPACES IN ACTION ON PRESSURELESS SYSTEMS ARISING FROM MODELS OF COLLECTIVE BEHAVIOR RAPHAËL DANCHIN, PIOTR BOGUSLAW MUCHA AND PATRICK TOLKSDORF - Archive ouverte HAL Access content directly
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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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Dates and versions

hal-02568285 , version 1 (08-05-2020)
hal-02568285 , version 2 (02-11-2020)

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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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