Abstract
We construct infinitely many incompressible Sobolev vector fields u∈CtWx1,p˜ on the periodic domain Td for which uniqueness of solutions to the transport equation fails in the class of densities ρ∈CtLxp, provided 1/p+1/p˜>1+1/d. The same result applies to the transport-diffusion equation, if, in addition, p′<d.
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Schedule a callMore From: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
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