Analyticity for the (generalized) Navier-Stokes equations with rough initial data

2013/10/08 by Huang, Chunyan, Wang, Baoxiang
#35K55 #35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.2141

Abstract

We study the Cauchy problem for the (generalized) incompressible Navier-Stokes equations u_t+(-Δ)^αu+u⋅ ∇ u +∇ p=0, \rm div u=0, u(0,x)= u₀. We show the analyticity of the local solutions of the Navier-Stokes equation (α=1) with any initial data in critical Besov spaces B^n/p-1_p,q(ℝⁿ) with 1< p

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