Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (6): 1741-1748.doi: 10.1016/S0252-9602(14)60119-3

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GLOBAL REGULARITY FOR MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATIONS

 YANG Wan-Rong, JIU Quan-Sen   

  1. Department of Mathematics, Beifang University of Nationalities, Ningxia 750021, China; Department of Mathematics, Capital Normal University, Beijing 100037, China
  • Received:2013-09-22 Revised:2014-05-18 Online:2014-11-20 Published:2014-11-20
  • Supported by:

    Jiu was supported by Project of Beijing Chang Cheng Xue Zhe (11228102), and was also supported by NSF of China (11171229, 11231006).

Abstract:

We consider the n-dimensional modified quasi-geostrophic (SQG) equations
tθ + u · ∇θ + Kαθ = 0,
u = ∧α−1R±θ

with K> 0, α∈ (0, 1] and θ0W1,∞(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

CLC Number: 

  • 35Q35
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