Global regularity of semi-critical case of anisotropic quasi-geostrophic equations in Sobolev spaces

2024/07/04 by Mustapha Amara, Amara, Mustapha
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2407.04090

openalex publication_date 2024/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the following anisotropic quasi-geostrophic equations *(AQG)_α,β ∂_tθ+ u_θ.∇θ+μ|∂₁|^2αθ+ν|∂₂|^2βθ=0, u_θ=R^⊥θ, where min\α,β\=(1)/(2) et max\α,β\∈ ((1)/(2),1). This equation is a particular case of the equation introduced by Ye (2019) in \citeYZ. In this paper, we prove that for any initial data θ⁰ in the Sobolev space H^s(ℝ²), s >1, the equation (AQG)_α,β has a global solution θ in C_b(ℝ⁺,H^s(ℝ²)).

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