2022/09/16 by Pham Truong Xuan, Xuan, Pham Truong, Ngoc, Tran Thi
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2209.07803
openalex publication_date 2022/09/16 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28
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.