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The global attractor of the 2D Boussinesq equations with fractional Laplacian in subcritical case. (English) Zbl 1352.35190

Authors’ abstract: We prove global well-posedness of strong solutions and existence of the global attractor for the 2D Boussinesq system in a periodic channel with fractional Laplacian in subcritical case. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and temperature.

MSC:

35Q86 PDEs in connection with geophysics
35R11 Fractional partial differential equations
34D45 Attractors of solutions to ordinary differential equations
35B32 Bifurcations in context of PDEs
86A05 Hydrology, hydrography, oceanography
86A10 Meteorology and atmospheric physics
35D35 Strong solutions to PDEs
26A33 Fractional derivatives and integrals
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