Entire solutions of hydrodynamical equations with exponential dissipation

Claude Bardos (1) , Uriel Frisch (2) , Walter Pauls (3) , Samriddhi sankar Ray (4) , Edriss S. Titi (5)

1 LJLL - Laboratoire Jacques-Louis Lions
2 Laboratoire Cassiopée
3 MPIDS - Max Planck Institute for Dynamics and Self-Organization
4 Center for Condensed Matter Theory, Department of Physics
5 DMDMAE - Department of Mathematics and Department of Mechanical and Aerospace Engineering

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially at high wavenumbers. We show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than exponential.

Domaines: Analyse numérique [cs.NA]

Claude Bardos, Uriel Frisch, Walter Pauls, Samriddhi sankar Ray, Edriss S. Titi. Entire solutions of hydrodynamical equations with exponential dissipation. Communications in Mathematical Physics, 2010, 293, pp.519-543. ⟨10.1007/s00220-009-0916-z⟩. ⟨hal-00392130⟩