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November  2013, 33(11&12): 5521-5523. doi: 10.3934/dcds.2013.33.5521

## An example of large global smooth solution of 3 dimensional Navier-Stokes equations without pressure

 1 Department of Mathematics, University of California, Other lines, Riverside, CA 92521, United States

Received  November 2011 Published  May 2013

We construct a global smooth solution of 3 dimensional Navier-Stokes equations in the torus, which also solves the heat equation. The solution is three dimensional and it can be arbitrarily large.
Citation: Qi S. Zhang. An example of large global smooth solution of 3 dimensional Navier-Stokes equations without pressure. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5521-5523. doi: 10.3934/dcds.2013.33.5521
##### References:
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##### References:
 [1] C. Foias and J.-C. Saut, Asymptotic behavior, as $t \to \infty$, of solutions of Navier-Stokes equations and nonlinear spectral manifolds, Indiana Univ. Math. J., 33 (1984), 459-477. doi: 10.1512/iumj.1984.33.33025. [2] Z. Lei, F. H. Lin and Y. Zhou, Private, communications., (). [3] G. Ponce, R. Racke, T. C. Sideris and E. S. Titi, Global stability of large solutions to the $3$D Navier-Stokes equations, Comm. Math. Phys., 159 (1994), 329-341. doi: 10.1007/BF02102642. [4] M. E. Schonbek, T. P. Schonbek and Endre Süli, Large-time behaviour of solutions to the magnetohydrodynamics equations, Math. Ann., 304 (1996), 717-756. doi: 10.1007/BF01446316.
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