Optimality of integrability estimates for advection-diffusion equations
نویسندگان
چکیده
We discuss L integrability estimates for the solution u of the advection-diffusion equation ∂t u + div (bu) = ∆ u, where the velocity field b ∈ Lt r Lx q . 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.
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