About the possibility of minimal blow up for Navier-Stokes solutions with data in H^s(R³)

2015/05/22 by Eugénie Poulon, Poulon, Eugénie
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1505.06197

arxiv created 2015/05/22 · openalex publication_date 2015/05/22 · arxiv updated 2015/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Considering initial data in H^s, with (1)/(2) \textless s \textless (3)/(2), this paper is devoted to the study of possible blowing-up Navier-Stokes solutions such that (T*(u_0) -t)^{(1)/(2) (s- (1)/(2))} ‖ u ‖_H^s is bounded. Our result is in the spirit of the tremendous works of L. Escauriaza, G. Seregin, and V. \breveSver\acuteak and I. Gallagher, G. Koch, F. Planchon, where they proved there is no blowing-up solution which remain bounded in L³(R³). The main idea is that if such blowing-up solutions exist, they satisfy critical properties.

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