论文标题
长时间的精制渐近线结合了3D轴向对称的Boussinesq系统，其热扩散率为零
A refined long time asymptotic bound for 3D axially symmetric Boussinesq system with zero thermal diffusivity
论文作者
论文摘要
在本文中，我们获得了与没有热扩散率的Boussinesq系统的全局轴向对称溶液的精致时间渐近上限。我们显示了速度的空间$ w^{1，p} $ - sobolev（$ 2 \ 2 \ leq p <\ infty $）规范，只能以$ t \ to+\ infty $的形式增长。在最初数据施加的签名潜在条件下，我们进一步得出上述规范始终均匀地界定。还给出了高阶估计：我们发现温度波动的$ H^1 $规范以$ t \ to+\ infty $的形式增长。同时，对于任何$ m \ geq 1 $，我们推断出解决方案的$ h^m $ - 量子增长比双重指数函数慢。结果，这些改善了\ cite {hr：2010aihp}的结果，其中作者只提供了粗糙的时间渐近上限，同时证明了全球范围的良好性。
In this paper, we obtain a refined temporal asymptotic upper bound of the global axially symmetric solution to the Boussinesq system with no thermal diffusivity. We show the spacial $W^{1,p}$-Sobolev ($2\leq p<\infty$) norm of the velocity can only grow at most algebraically as $t\to+\infty$. Under a signed potential condition imposed on the initial data, we further derive that the aforementioned norm is uniformly bounded at all times. Higher order estimates are also given: We find the $H^1$ norm of the temperature fluctuation grows sub-exponentially as $t\to+\infty$. Meanwhile, for any $m\geq 1$, we deduce that the $H^m$-temporal growth of the solution is slower than a double exponential function. As a result, these improve the results in \cite{HR:2010AIHP} where the authors only provided rough temporal asymptotic upper bounds while proving the global well-posedness.
