suitable weak solutions
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Author(s):  
Francesca Crispo ◽  
Paolo Maremonti

AbstractThe paper is concerned with the Navier–Stokes Cauchy problem. We investigate on some results of regularity and uniqueness related to suitable weak solutions corresponding to a special set of initial data. The suitable weak solution notion is meant in the sense introduced by Caffarelli–Kohn–Nirenberg. As further result we discuss the uniqueness of a set of suitable weak solutions (wider than the previous one) enjoying a “Prodi–Serrin” condition which is “relaxed” in space.


Author(s):  
Kyungkeun Kang ◽  
Hideyuki Miura ◽  
Tai-Peng Tsai

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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