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.

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.

A simple proof of existence of weak and statistical solutions of Navier–Stokes equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 1-11 ◽  
Keyword(s):  
Weak Solution ◽  
Initial Data ◽  
Natural Number ◽  
Simple Proof ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Existence Proofs ◽  
Statistical Solutions

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.

scholarly journals On the construction of suitable weak solutions to the 3D Navier–Stokes equations in a bounded domain by an artificial compressibility method

2017 ◽  
Vol 20 (01) ◽  
pp. 1650064 ◽  
Author(s):  
Luigi C. Berselli ◽  
Stefano Spirito
Keyword(s):  
Bounded Domain ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Bounded Domains ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Artificial Compressibility Method

We prove that suitable weak solutions of 3D Navier–Stokes equations in bounded domains can be constructed by a particular type of artificial compressibility approximation.

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