| Abstract: |
| We prove existence results for the Cauchy--Dirichlet problem for convection--diffusion parabolic systems with singular coefficients in the convective term. The principal part of our operator is of $p$-Laplacian type and standard monotonicity and growth conditions are assumed. However, the coefficients of the lower order terms are time dependent and belong to borderline mixed Lebesgue--Marcinkiewicz spaces, and this causes lack of coercivity. We are not assuming any additional structure condition, such as for example the well-known Landes condition, introduced to deal with systems. We also show optimality of our results in the linear case. |
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