Differential and Integral Equations
- Differential Integral Equations
- Volume 10, Number 5 (1997), 961-974.
Smooth solutions of the vector Burgers equation in nonsmooth domains
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 (, ) 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.
Differential Integral Equations, Volume 10, Number 5 (1997), 961-974.
First available in Project Euclid: 1 May 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76D05: Navier-Stokes equations [See also 35Q30]
Heywood, John G.; Xie, Wenzheng. Smooth solutions of the vector Burgers equation in nonsmooth domains. Differential Integral Equations 10 (1997), no. 5, 961--974. https://projecteuclid.org/euclid.die/1367438628