三维随机本原方程组在Fourier-Besov空间中解的整体存在性

Global Existence of Three-Dimensional Stochastic Primitive Equations in Fourier-Besov Spaces

摘要: 众所周知，三维随机本原方程组是描述大气和海洋动力学行为的基本方程组，本文将主要研究其初值问题解的整体存在性理论。首先，运用Littlewood-Paley理论和Bony仿积分解技巧，建立了Stokes-Coriolis-Stratification半群新的双线性估计。然后，建立相应随机线性初值问题解的有界性估计，结合叠加原理以及不动点定理，在小初值和小随机外力的假设条件下，证明了三维随机本原方程组在Fourier-Besov空间中温和解的整体存在性和唯一性。本文的主要结果是对经典三维本原方程组初值问题解的整体存在性理论在随机情形下的推广。

Abstract: This paper is devoted to studying the global existence of solutions to initial value problem of the three-dimensional stochastic primitive equations, which are a basic system that is usually used to describe the dynamic behavior of the atmospheric and the oceanic ows. Firstly, by using the Littlewood-Paley theory and Bony para-product decomposition technique, we establish a new bilinear estimation for the Stokes-Coriolis-Stratification semigroup. Then, by establishing the boundedness estimations for solutions of the corresponding stochastic linear initial value problem, and combining the superposition principle and Banach's fixed point theorem, we prove the global existence and uniqueness of mild solutions to the three-dimensional stochastic primitive equations with small initial values and small random external forces in the Fourier-Besov space frame. Our main result is a generalization of the global existence of the solutions for the initial value problem of the classical three-dimensional primitive equations under the stochastic case.