부산대학교 도서관

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.na.2006.03.030 Byline: Eric Olson (a)(b), Edriss S. Titi (a)(c)(d) Abstract: We study global well-posedness and regularity of solutions for a family of incompressible three-dimensional Navier-Stokes-alpha-like models that employ fractional Laplacian operators. This family of equations depends on two parameters, I[cedilla].sub.1 and I[cedilla].sub.2, which affect the strength of non-linearity (vorticity stretching) and the degree of viscous smoothing. Varying I[cedilla].sub.1 and I[cedilla].sub.2 interpolates between the incompressible Navier-Stokes equations and the incompressible (Lagrangian averaged) Navier-Stokes-[alpha] model. Our main result, which contains previously established results of J.L. Lions and others, provides a relationship between I[cedilla].sub.1 and I[cedilla].sub.2 that is sufficient to guarantee global existence, uniqueness and regularity of solutions. Author Affiliation: (a) Department of Mathematics, University of California, Irvine, CA 92697, USA (b) Department of Mathematics, University of Nevada, Reno, NV 89557, USA (c) Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA (d) Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel Article History: Received 19 July 2005; Accepted 20 March 2006