Abstract
This paper focuses on the global existence of strong solutions to the magnetic Bénard problem with fractional dissipation and without thermal diffusion inℝdwithd≥3. By using the energy method and the regularization of generalized heat operators, we obtain the global regularity for this model under minimal amount dissipation.
Highlights
Consider the global well-posedness problem to the d-dimensional magnetic Benard problem ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨ ztu ztb + + u u · ·∇u ∇b μΛ2αu − ]Λ2βb b ∇p + · ∇u, b · ∇b +
We prove eorem 1
We only prove Proposition 1 for the case α + β 1 + d/2
Summary
Is paper focuses on the global existence of strong solutions to the magnetic Benard problem with fractional dissipation and without thermal diffusion in Rd with d ≥ 3. By using the energy method and the regularization of generalized heat operators, we obtain the global regularity for this model under minimal amount dissipation
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