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Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation

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  • We give existence and uniqueness results of the weak-renormalized solution for a class of nonlinear Boussinesq's systems. The main tools rely on regularity results for the Navier-Stokes equations with precise estimates on the solution with respect to the data in dimension $2$ and on the techniques involved for renormalized solutions of parabolic problems.
    Mathematics Subject Classification: Primary: 35Q35; Secondary: 35D05, 35D30, 76D03.


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