Differential and Integral Equations

Concerning the regularity of the solutions to the Navier-Stokes equations via the truncation method. I

H. Beirão da Veiga

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Abstract

In view of the lack of a global regularity theorem for the solutions $(v,p)$ of the Navier-Stokes equations there has been a great deal of activity in establishing sufficient conditions on the velocity $v$ in order to guarantee the regularity of the solution. However, nontrivial conditions involving the pressure seem not to be available in the literature. In this paper we present a sharp sufficient condition involving a combination of $v$ and $p$. The proof relies on the truncation method, introduced in reference [3] for studying scalar elliptic equations and developed further by many authors (see, in particular [6] and [4]). In the sequel we use some basic results proved in [4].

Article information

Source
Differential Integral Equations, Volume 10, Number 6 (1997), 1149-1156.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367438225

Mathematical Reviews number (MathSciNet)
MR1608053

Zentralblatt MATH identifier
0940.35154

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10]
Secondary: 35B65: Smoothness and regularity of solutions 35J99: None of the above, but in this section 76D05: Navier-Stokes equations [See also 35Q30]

Citation

Beirão da Veiga, H. Concerning the regularity of the solutions to the Navier-Stokes equations via the truncation method. I. Differential Integral Equations 10 (1997), no. 6, 1149--1156. https://projecteuclid.org/euclid.die/1367438225


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