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Global smooth solution for the 3D generalized tropical climate model with partial viscosity and damping

Hui Liu, Chengfeng Sun, Mei Li

Abstract

The three-dimensional generalized tropical climate model with partial viscosity and damping is considered in this paper. Global well-posedness of solutions of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved for $α\geq\frac{3}{2}$ and $β\geq4$. Global smooth solution of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved in $H^s(\mathbb R^3)$ $(s>2)$ for $α\geq\frac{3}{2}$ and $4\leqβ\leq5$.

Global smooth solution for the 3D generalized tropical climate model with partial viscosity and damping

Abstract

The three-dimensional generalized tropical climate model with partial viscosity and damping is considered in this paper. Global well-posedness of solutions of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved for and . Global smooth solution of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved in for and .
Paper Structure (4 sections, 2 theorems, 93 equations)

This paper contains 4 sections, 2 theorems, 93 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of Theorem \ref{['the']}
  4. Proof of Theorem \ref{['the1']}

Key Result

Theorem 2.1

Let $u_{0}\in H^{0,1}(\mathbb{R}^{3})$ and $v_{0}\in H^{1}(\mathbb{R}^{3})$ and $\theta_{0}\in H^{1}(\mathbb{R}^{3})$ with $\nabla\cdot u_{0}=0$, $\alpha\geq\frac{3}{2}$ and $\beta\geq4$. The system (1) has a unique global solution $(u,v,\theta)$ satisfying and

Theorems & Definitions (3)

  • Theorem 2.1
  • Theorem 2.2
  • Remark 4.1