Vanishing viscosity limit for an expanding domain in space

Details Vanishing viscosity limit for an expanding domain in space Vanishing viscosity limit for an expanding domain in space

2008-10-17

arxiv.org/abs/0810.3255v1

Ann. IHP Anal non-Lin. 26 (2009), 2521-2537

Mathematics

Analysis of PDEs

23 pages, submitted for publication

Scientific paper

10.1016/j.anihpc.2009.07.007

We study the limiting behavior of viscous incompressible flows when the fluid domain is allowed to expand as the viscosity vanishes. We describe precise conditions under which the limiting flow satisfies the full space Euler equations. The argument is based on truncation and on energy estimates, following the structure of the proof of Kato's criterion for the vanishing viscosity limit. This work complements previous work by the authors, see [Kelliher, Comm. Math. Phys. 278 (2008), 753-773] and [arXiv:0801.4935v1].

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