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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.

35B45 A priori estimates in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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