论文标题
BousSinesQ系统在实际双曲线歧管上的良好性和指数稳定性
Wellposedness and exponential stability for Boussinesq systems on real hyperbolic Manifolds
论文作者
论文摘要
我们研究了$ l^p $ - 相位在实际双曲线歧管$ \ mathbb {h}^d（\ mathbb {r}）$的框架上，在$ l^p $ - 相位空间中对BousSinesQ系统的全球存在和指数衰减。我们考虑了Ebin-Marsden的几个Laplace和Laplace-Beltrami运算符，与相应的线性系统相关联，该系统提供了矢量矩阵Semigoup。首先，我们通过使用矢量矩阵半群的分散和平滑估计值来显示线性系统中有界温和解决方案的独特性。接下来，使用固定点参数，我们可以从线性系统传递到半线性系统，以确定有限的温和解决方案的存在。由于Gronwall的不平等，我们将阐明此类解决方案的指数稳定性。最后，我们将稳定性应用于BousSinesQ系统的周期性温和解决方案的存在。
We investigate the global existence and exponential decay of mild solutions for the Boussinesq systems in $L^p$-phase spaces on the framework of real hyperbolic manifold $\mathbb{H}^d(\mathbb{R})$, where $d \geqslant 2$ and $1<p\leq d$. We consider a couple of Ebin-Marsden's Laplace and Laplace-Beltrami operators associated with the corresponding linear system which provides a vectorial matrix semigoup. Primarily, we show the existence and the uniqueness of the bounded mild solution for the linear system by using dispersive and smoothing estimates of the vectorial matrix semigroup. Next, using the fixed point arguments, we can pass from the linear system to the semilinear system to establish the existence of the bounded mild solutions. Due to Gronwall's inequality, we will clarify the exponential stability of such solutions. Finally, we give an application of stability to the existence of periodic mild solutions for the Boussinesq systems.
