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1997 Smooth solutions of the vector Burgers equation in nonsmooth domains
John G. Heywood, Wenzheng Xie
Differential Integral Equations 10(5): 961-974 (1997).


We prove the existence and uniqueness of smooth solutions of the vector Burgers equation in arbitrary two- and three-dimensional domains. The only assumption about the spatial domain is that it should be an open set. The underlying estimates for these results are proved using new "elliptic-Sobolev" inequalities of Xie ([13], [15]) for the Laplacian. Our purpose in giving these results is to develop methods that we think can be eventually transferred to the Navier-Stokes equations. Indeed, the only missing point is the proof of analogous "elliptic-Sobolev" inequalities for the Stokes operator, which we conjecture to be valid.


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John G. Heywood. Wenzheng Xie. "Smooth solutions of the vector Burgers equation in nonsmooth domains." Differential Integral Equations 10 (5) 961 - 974, 1997.


Published: 1997
First available in Project Euclid: 1 May 2013

zbMATH: 0891.35136
MathSciNet: MR1741761

Primary: 35Q53
Secondary: 76D03 , 76D05

Rights: Copyright © 1997 Khayyam Publishing, Inc.


Vol.10 • No. 5 • 1997
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