Viscosity versus vorticity stretching: Global well-posedness for a family of Navier-Stokes-alpha-like models

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, 1 and 2, which affect the strength of non-linearity (vorticity stretching) and the degree of viscous smoothing. Varying 1 and 2 interpolates between the incompressible Navier-Stokes equations and the incompressible (Lagrangian averaged) Navier-Stokes- model. Our main result, which contains previously established results of J.L. Lions and others, provides a relationship between 1 and 2 that is sufficient to guarantee global existence, uniqueness and regularity of solutions. 2006 Elsevier Ltd. All rights reserved.

authors

• Titi, Edriss

published proceedings

• NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

author list (cited authors)

• Olson, E., & Titi, E. S.

citation count

• 45

complete list of authors

• Olson, Eric||Titi, Edriss S

publication date

• June 2007

publisher

• Elsevier  Publisher

published in

• Nonlinear Analysis Theory Methods and Applications  Journal

keywords

• Existence
• Fluid Mechanics
• Regularity Theory
• Turbulence
• Uniqueness

Digital Object Identifier (DOI)

• 10.1016/j.na.2006.03.030

start page

• 2427

end page

• 2458

volume

• 66

issue

• 11

URL

• http://dx.doi.org/10.1016/j.na.2006.03.030