论文标题
水平周期性带状域中的线性分层的BousSinesQ方程的渐近稳定性和尖锐的衰减速率
Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain
论文作者
论文摘要
我们考虑在没有速度阻尼或速度扩散的情况下，在水平周期性周期性带状条件下，在没有速度阻尼或速度扩散的情况下，在没有速度阻尼或速度扩散的情况下，多维BousSinesQ方程的初始边界值问题。我们证明了在高阶Sobolev空间中证明经典解决方案的全球存在，这些空间满足了线性分层平衡周围的高阶兼容性条件，温度融合到渐近型剖面以及速度场的敏捷衰减速率和基于能量估计的所有中间规范中的速度场和温度波动的敏锐衰减速率。据我们所知，我们的结果为所有中间规范中的温度波动和垂直速度提供了首个尖锐的衰减速率。
We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms.
