Global well-posedness for a Modified 2D dissipative quasi-geostrophic equation with initial data in the critical Sobolev space H¹

2009/10/06 by May, Ramzi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.0998

Abstract

In this paper, we consider the following modified quasi-geostrophic equations ∂_tθ+Λ^αθ+u∇θ=0, u=Λ^α-1R^⊥(θ) where α∈ ]0,1[ is a fixed parameter. This equation was recently introduced by P. Constantin, G. Iyer and J. Wu in \citeCIW as a modification of the classical quasi-geostrophic equation. In this paper, we prove that for any initial data θ_∗ in the Sobolev space H¹(ℝ²), the equation (MQG) has a global and smooth solution θ in C(ℝ⁺,H¹(ℝ²)) .

Related

• Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
• Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness
• A Remark on the Global Well-posedness of a Modified Critical Quasi-geostrophic Equation
• Global solutions to the dissipative quasi-geostrophic equation with dispersive forcing
• On the global well-posedness of the critical quasi-geostrophic equation