Advances in Differential Equations

Solutions of the Navier-Stokes equations for large oscillatory data

Igor Kukavica, Walter Rusin, and Mohammed Ziane

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Abstract

We address global regularity of solutions of the Navier--Stokes equations in a periodic domain $Q=[0,1]^3$. We prove that, in the class of solutions oscillating in the vertical direction, the global solutions are smooth under natural conditions on the derivatives in the horizontal direction and the vertical and horizontal averages of the initial data. There are no restrictions on the size of the data.

Article information

Source
Adv. Differential Equations Volume 18, Number 5/6 (2013), 549-586.

Dates
First available in Project Euclid: 14 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1363266257

Mathematical Reviews number (MathSciNet)
MR3086465

Zentralblatt MATH identifier
1264.35165

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35K15: Initial value problems for second-order parabolic equations

Citation

Kukavica, Igor; Rusin, Walter; Ziane, Mohammed. Solutions of the Navier-Stokes equations for large oscillatory data. Adv. Differential Equations 18 (2013), no. 5/6, 549--586. https://projecteuclid.org/euclid.ade/1363266257.


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