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Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients. (English) Zbl 1098.35038
The aim of the paper is to give estimates of conservation or loss of regularity for the initial data of transport-diffusion equations $$\partial_tf+v\nabla f -\nu\Delta f= g$$. The regularity is described in terms of inhomogeneous Besov spaces. Roughly speaking if $$\nabla v$$ belongs to $$L^1(0,T;L^\infty)$$ then the regularity of initial data is preserved. If $$\nabla v$$ is less regular then the regularity may coarsen with time.

##### MSC:
 35B45 A priori estimates in context of PDEs 35Q35 PDEs in connection with fluid mechanics
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##### References:
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