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A regularity criterion for the 3D axisymmetric Boussinesq equations with non-zero swirl

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In this paper, we are devoted to establishing a new regularity criterion of weak solutions to incompressible axisymmetric Boussinesq equations. More precisely, we prove that for a small ϵ >… Click to show full abstract

In this paper, we are devoted to establishing a new regularity criterion of weak solutions to incompressible axisymmetric Boussinesq equations. More precisely, we prove that for a small ϵ > 0, if the angular component of velocity field uθ(t, r, z) satisfies sup0 0, which is independent of the initial data, then the weak solution (u, ρ) to 3D Boussinesq equations is regular in (0, T].

Keywords: regularity criterion; boussinesq equations; boussinesq; axisymmetric boussinesq

Journal Title: Journal of Mathematical Physics
Year Published: 2023

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