论文标题
关于Besove方程的薄弱解决方案的规律性
On the regularity of weak solutions of the Boussinesq equations in Besov spaces Dedicated to Enrique Zuazua on the occasion of his sixtieth birthday
论文作者
论文摘要
本文解决的主要问题涉及Z. Zhang对结果的扩展，他在同质的BESOV空间$ \ dot {b} _ {\ infty，\ infty} ^{ - 1}（ - 1}（\ Mathbb {r}％ ^{3}）的情况{eq1.1}）以下（从$ h^{2} $中的初始数据开始，以至于$％（\ nabla u，\ nabla u，\nablaθ）\ in l^{2} \ left（0，t; \ dot; \ dot; \ dot {b} _ {b} _ { \ Mathbb {r}^{3}）\ right）$，那么解决方案在$ t $之后永远保持平稳。在此贡献中，我们仅通过假设速度$ u $而不是温度$θ$的条件来证明弱解决方案的结果相同。
The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space $\dot{B}_{\infty ,\infty }^{-1}(\mathbb{R}% ^{3})$, that, if the solution of the Boussinesq equation (\ref% {eq1.1}) below (starting with an initial data in $H^{2}$) is such that $% (\nabla u,\nabla θ)\in L^{2}\left( 0,T;\dot{B}_{\infty ,\infty }^{-1}(% \mathbb{R}^{3})\right)$, then the solution remains smooth forever after $T$. In this contribution, we prove the same result for weak solutions just by assuming the condition on the velocity $u$ and not on the temperature $θ$.
