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On the global well-posedness of the Euler-Boussinesq system with fractional dissipation. (English) Zbl 1194.35329
Summary: We study the global well-posedness of the Euler-Boussinesq system with the term dissipation \(|D|^{\alpha }\) on the temperature equation. We prove that for \(\alpha >1\) the coupled system has a global unique solution for initial data with critical regularities.

MSC:
35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs
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