关键词: quasi-geostrophic equations, global regularity, maximum principle

Abstract:

We consider the n-dimensional modified quasi-geostrophic (SQG) equations
∂_tθ + u · ∇_θ + K∧^αθ = 0,
u = ∧^α−1R^±θ

with K> 0, α∈ (0, 1] and θ₀ ∈ W^1,∞(Rⁿ). In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu[5], who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case. The proof provided in this paper is based on the nonlinear maximum principle as well as the
approach in Constantin and Vicol [2].

Key words: quasi-geostrophic equations, global regularity, maximum principle