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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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

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

First available in Project Euclid: 14 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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