The Lorenz equation as a metaphor for the Navier-Stokes equations Academic Article

abstract

• Three approaches for the rigorous study of the 2D Navier-Stokes equations (NSE) are applied to the Lorenz system. Analysis of time averaged solutions leads to a description of invariant probability measures on the Lorenz attractor which is much more complete than what is known for the NSE. As is the case for the NSE, solutions on the Lorenz attractor are analytic in a strip about the real time axis. Rigorous estimates are combined with numerical computation of Taylor coefficients to estimate the width of this strip. Approximate inertial forms originally developed for the NSE are analyzed for the Lorenz system, and the dynamics for the latter are completely described.

authors

• Titi, Edriss

published proceedings

• DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

author list (cited authors)

• Foias, C., Jolly, M. S., Kukavica, I., & Titi, E. S.

citation count

• 15

complete list of authors

• Foias, C||Jolly, MS||Kukavica, I||Titi, ES

publication date

• January 2001

publisher

• American Institute of Mathematical Sciences (AIMS)  Publisher

published in

• Discrete and Continuous Dynamical Systems Series A  Journal

keywords

• Lorenz Equation
• Navier-stokes
• Statistical Solutions

Digital Object Identifier (DOI)

• 10.3934/dcds.2001.7.403

start page

• 403

end page

• 429

volume

• 7

issue

• 2

URL

• http://dx.doi.org/10.3934/dcds.2001.7.403