Ill-posedness of Naiver-Stokes equations and critical Besov-Morrey spaces

2017/06/25 by Qixiang Yang, Haibo Yang, Yang, Qixiang +3
Mathematics · #35Q30 #76D03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1706.08120

openalex publication_date 2017/06/25 · openalex created_date 2017/06/30 · openalex updated_date 2026/07/28

Abstract

The blow up phenomenon in the first step of the classical Picard's scheme was proved in this paper. For certain initial spaces, Bourgain-Pavlović and Yoneda proved the ill-posedness of the Navier-Stokes equations by showing the norm inflation in certain solution spaces. But Chemin and Gallagher said the space B^-1,∞_∞ seems to be optimal for some solution spaces best chosen. In this paper, we consider more general initial spaces than Bourgain-Pavlović and Yoneda did and establish ill-posedness result independent of the choice of solution space. Our result is a complement of the previous ill-posedness results on Navier-Stokes equations.

Citations

• On the solutions of quasi-linear elliptic partial differential equations

Related

• Ill-posedness for the Navier-Stokes equations in critical Besov spaces\n B^-1_\∞,q
• Ill-posedness of the Navier-Stokes equations in a critical space in 3D
• Sharp well-posedness and ill-posedness of the Navier-Stokes initial value problem in Besov-type spaces
• Ill-posedness for the 3D inhomogeneous Navier-Stokes equations in the critical Besov space near L⁶ framework
• On the ill-posedness for the Navier--Stokes equations in the weakest Besov spaces