Volume no :62, Issue no: 1, May (2020)

Journal of Mathematical Sciences: Advances and Applications

A LOCAL STRONG SOLUTION OF THE NAVIER-STOKES PROBLEM IN

Author's: Maoting Tong and Daorong Ton
Pages: [1] - [19]
Received Date: March 21, 2020; Revised May 8, 2020
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122125

Abstract

In this paper, we prove that the Navier-Stokes initial value problem (1) has a unique smooth local strong solution and if the following condition are satisfied:
(1) and f is Hölder continuous about t on
(2) The initial value is smooth, divergence-free vector field.

Keywords

Navier-Stokes equation, existence and uniqueness, local solution, semigroup of operators, invariance, Banach lattice, fractional powers.