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

الأصل · EN

In this paper, we consider the following modified quasi-geostrophic equations ∂ₜθ+Λαθ+u∇θ=0, u=Λα⁻¹R⊥(θ) where α∈]0,1[is a fixed parameter. This equation was recently introduced by P. Constantin, G. Iyer and J. Wu in CIW 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)).