Long-time behavior of global solutions of anisotropic quasi-geostrophic equations in Sobolev space

2022/01/26 by Amara, Mustapha
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.10840

Abstract

We study the behavior at infinity in time of the global solution of the anisotropic quasi-geostrophic equation θ∈ C_b(ℝ⁺,H^s( ℝ²)). We prove that this solution decays to zero as time goes to infinity in L^p(ℝ²), p∈ [2,+∞], moreover, we prove also that lim_{t→ +∞}‖θ(t)‖_H^s=0.

Related

• Global regularity of semi-critical case of anisotropic quasi-geostrophic equations in Sobolev spaces
• Global solution of anisotropic Quasi-Geostrophic Equations in Sobolev Space
• Asymptotic study of supercritical surface Quasi-Geostrophic equation in critical space
• Existence and Uniqueness of the Solution to the Anisotropic Quasi-Geostrophic Equations in the Sobolev Space
• On the boundedness of the global solution of anisotropic quasi-geostrophic equations in Sobolev space