We discuss Lp integrability estimates for the solution u of the advection-diffusion equation ∂tu+div(bu)=Δu, where the velocity field b∈LrtLqx. We first summarize some classical results proving such estimates for certain ranges of the exponents r and q. Afterwards we prove the optimality of such ranges by means of new original examples.

Optimality of integrability estimates for advection-diffusion equations / Bianchini, Stefano; Colombo, Maria; Crippa, Gianluca; Spinolo, Laura V.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 24:4(2017), pp. 1-19. [10.1007/s00030-017-0455-9]

Optimality of integrability estimates for advection-diffusion equations

Bianchini, Stefano;
2017-01-01

Abstract

We discuss Lp integrability estimates for the solution u of the advection-diffusion equation ∂tu+div(bu)=Δu, where the velocity field b∈LrtLqx. We first summarize some classical results proving such estimates for certain ranges of the exponents r and q. Afterwards we prove the optimality of such ranges by means of new original examples.
2017
24
4
1
19
33
https://doi.org/10.1007/s00030-017-0455-9
https://link.springer.com/article/10.1007/s00030-017-0455-9
https://arxiv.org/abs/1702.00321
Bianchini, Stefano; Colombo, Maria; Crippa, Gianluca; Spinolo, Laura V.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/59960
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