Remark on uniqueness of weak solutions to the Navier–Stokes equations

Analysis ◽  
2008 ◽  
Vol 28 (1) ◽  
Author(s):  
Sadek Gala ◽  
Samia Benbernou
Keyword(s):  
Initial Data ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Consider the Navier–Stokes equations with the initial data a ∈

scholarly journals Short Time Regularity of Navier–Stokes Flows with Locally L3 Initial Data and Applications

2020 ◽  
Author(s):  
Kyungkeun Kang ◽  
Hideyuki Miura ◽  
Tai-Peng Tsai
Keyword(s):  
Initial Data ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Suitable Weak Solutions ◽  
Stokes Flows ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
Similar Solutions ◽  
Short Time

Abstract We prove short time regularity of suitable weak solutions of 3D incompressible Navier–Stokes equations near a point where the initial data is locally in $L^3$. The result is applied to the regularity problems of solutions with uniformly small local $L^3$ norms and of forward discretely self-similar solutions.

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