论文标题
Boussinesq系统在非紧凑型riemannian歧管上的广义重力场和适合
Generalized gravitational fields and well-posedness of the Boussinesq systems on non-compact Riemannian Manifolds
论文作者
论文摘要
我们研究温和解决方案在非紧缩利曼尼亚歧管框架上配备有广义重力场的BousSinesQ系统的全球存在，独特性和指数稳定性。我们处理一些满足曲率张量的有界和负面条件的歧管。我们考虑了与相应的线性系统相关的几个stokes和热半群，该线性系统提供了矢量矩阵半群。通过使用矢量矩阵半群的分散和平滑估计，我们建立了线性系统中温和解决方案的全球存在和唯一性。接下来，我们可以通过使用固定点参数从线性系统传递到半线性系统，以获得良好的。此外，我们将通过使用Gronwall的不平等来证明此类解决方案的指数稳定性。
We study the global existence, uniqueness and exponential stability of mild solutions to the Boussinesq systems equipped with a generalized gravitational field on the framework of non-compact Riemannian manifolds. We work on some manifolds satisfying some bounded and negative conditions on curvature tensors. We consider a couple of Stokes and heat semigroups associated with the corresponding linear system which provides a vectorial matrix semigoup. By using dispersive and smoothing estimates of the vectorial matrix semigroup we establish the global-in-time existence and uniqueness of mild solutions for linear systems. Next, we can pass from the linear system to the semilinear systems to obtain the well-posedness by using fixed point arguments. Moreover, we will prove the exponential stability of such solutions by using Gronwall's inequality.
