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.File in questo prodotto:
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