scholarly journals A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem

2017 ◽  
Vol 37 (3) ◽  
pp. 1283-1294 ◽  
Author(s):  
Francesca Crispo ◽  
◽  
Paolo Maremonti
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Partial Regularity ◽  
Navier Stokes ◽  
Suitable Weak Solution

scholarly journals On the uniqueness of a suitable weak solution to the Navier–Stokes Cauchy problem

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Francesca Crispo ◽  
Paolo Maremonti
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Initial Data ◽  
Weak Solutions ◽  
Navier Stokes ◽  
Suitable Weak Solution ◽  
Suitable Weak Solutions

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.

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