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Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients.

Raphaël Danchin (2005)

Revista Matemática Iberoamericana

This paper aims at giving an overview of estimates in general Besov spaces for the Cauchy problem on t = 0 related to the vector field ∂t + v·∇. The emphasis is on the conservation or loss of regularity for the initial data.When ∇u belongs to L1(0,T; L∞) (plus some convenient conditions depending on the functional space considered for the data), the initial regularity is preserved. On the other hand, if ∇v is slightly less regular (e.g. ∇v belogs to some limit space for which the embedding in L∞...

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