Produção Nacional
Revisado por pares
Navier–Stokes equations: local existence, uniqueness and blow-up of solutions in Sobolev–Gevrey spaces
2019; Taylor & Francis; Volume: 100; Issue: 9 Linguagem: Inglês
10.1080/00036811.2019.1671974
ISSN1563-504X
AutoresWilberclay G. Melo, Natã Firmino Rocha, Ezequiel Barbosa,
Tópico(s)Nonlinear Partial Differential Equations
ResumoThis work establishes local existence and uniqueness as well as blow-up criteria for solutions u(x,t) of the Navier–Stokes equations in Sobolev–Gevrey spaces Ha,σs(R3). More precisely, if it is assumed that the initial data u0 belongs to Ha,σs0(R3), with s0∈(12,32), we prove that there is a time T>0 such that u∈C([0,T];Ha,σs(R3)) for a>0,σ≥1 and s≤s0. If the maximal time interval of existence of solutions is finite, 0≤t<T∗, then, we prove, for example, that the blow-up inequality C1exp{C2(T∗−t)p}(T∗−t)−q≤∥u(t)∥Ha,σs(R3),q=2(sσ+σ0)+16σ,p=−13σ, holds for 0≤t 0, σ>1 (2σ0 is the integer part of 2σ).
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