Global Existence of Solutions to the 2D subcritical dissipative Quasi-Geostrophic equation and persistency of the initial regularity

2009/08/03 by May, Ramzi, Zahrouni, Ezzeddine
#35Q35 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0908.0199

Abstract

In this paper, we prove that if the initial data θ₀ and its Riesz transforms (R₁(θ₀) and R₂(θ₀)) belong to the space (S(ℝ²))^B_∞^1-2α,∞, where α∈ ]1/2,1[, then the 2D Quasi-Geostrophic equation with dissipation α has a unique global in time solution θ. Moreover, we show that if in addition θ₀ ∈ X for some functional space X such as Lebesgue, Sobolev and Besov's spaces then the solution θ belongs to the space C([0,+∞ [,X).

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