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

Título inglés	Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients.
Título español	Estimaciones en espacios de Besov para ecuaciones de transporte y transporte-difusión con coeficientes casi Lipschitz.
Autor/es	Danchin, Raphaël
Organización	Cent. Math. Univ. París 12, Créteil, Francia
Revista	0213-2230
Publicación	2005, 21 (3): 863-888, 19 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	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·Ñ. The emphasis is on the conservation or loss of regularity for the initial data. When Ñu 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 Ñv is slightly less regular (e.g. Ñv belogs to some limit space for which the embedding in L∞ fails), the regularity may coarsen with time. Different scenarios are possible going from linear to arbitrary small loss of regularity. This latter result will be used in a forthcoming paper to prove global well-posedness for two-dimensional incompressible density-dependent viscous fluids (see [11]). Besides, our techniques enable us to get estimates uniformly in v ≥ 0 when adding a diffusion term -vΔu to the transport equation.
Clasificación UNESCO	120220
Palabras clave español	Ecuaciones diferenciales hiperbólicas ; Problema de Cauchy ; Ecuación de difusión ; Fenómenos de transporte ; Espacios de Besov
Código MathReviews	MR2231013
Código Z-Math	Zbl 1098.35038
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