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Regularity Criterion for 3D Boussinesq Equations via Partial Horizontal Derivatives of Two Velocity Components
Bulletin of the Brazilian Mathematical Society, New Series ( IF 0.9 ) Pub Date : 2020-02-18 , DOI: 10.1007/s00574-020-00200-1 Fan Wu
Bulletin of the Brazilian Mathematical Society, New Series ( IF 0.9 ) Pub Date : 2020-02-18 , DOI: 10.1007/s00574-020-00200-1 Fan Wu
In this paper, a logarithmically improved regularity criterion for the incompressible Boussinesq equations is established via partial horizontal derivatives of two velocity components. It is shown that if the partial horizontal derivatives of two velocity components satisfy $$\begin{aligned} \int _{0}^{T} \frac{\big \Vert \left( \partial _1u_1, \partial _2u_2\right) \left( \cdot , t\right) \big \Vert _{\dot{\mathcal {M}}_{p,\frac{3}{r}}}^{\frac{2}{2-r}}}{1+\ln \left( e+\Vert u(\cdot , t)\Vert _{L^{4}}\right) } {\mathrm {d}} t<\infty \quad \text {with}\quad 0
中文翻译：
通过两个速度分量的偏水平导数的 3D Boussinesq 方程的正则性判据
本文通过两个速度分量的偏水平导数，建立了不可压缩Boussinesq方程的对数改进正则性判据。表明如果两个速度分量的偏水平导数满足 $$\begin{aligned} \int _{0}^{T} \frac{\big \Vert \left( \partial _1u_1, \partial _2u_2\right ) \left( \cdot , t\right) \big \Vert _{\dot{\mathcal {M}}_{p,\frac{3}{r}}}^{\frac{2}{2- r}}}{1+\ln \left( e+\Vert u(\cdot , t)\Vert _{L^{4}}\right) } {\mathrm {d}} t<\infty \quad \文本 {with}\quad 0
更新日期：2020-02-18
中文翻译：
通过两个速度分量的偏水平导数的 3D Boussinesq 方程的正则性判据
本文通过两个速度分量的偏水平导数，建立了不可压缩Boussinesq方程的对数改进正则性判据。表明如果两个速度分量的偏水平导数满足 $$\begin{aligned} \int _{0}^{T} \frac{\big \Vert \left( \partial _1u_1, \partial _2u_2\right ) \left( \cdot , t\right) \big \Vert _{\dot{\mathcal {M}}_{p,\frac{3}{r}}}^{\frac{2}{2- r}}}{1+\ln \left( e+\Vert u(\cdot , t)\Vert _{L^{4}}\right) } {\mathrm {d}} t<\infty \quad \文本 {with}\quad 0
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