Abstract
We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime L 2 weak limit of Leray–Hopf weak solutions of the Navier–Stokes equations on any bounded domain Ω ⊂ R d , d= 2 , 3 is a weak solution of the Euler equations. This holds for both no-slip and Navier friction conditions with viscosity-dependent slip length. The result allows for the emergence of non-unique, possibly dissipative, limiting weak solutions of the Euler equations.
Original language | English (US) |
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Pages (from-to) | 709-721 |
Number of pages | 13 |
Journal | Journal of Nonlinear Science |
Volume | 29 |
Issue number | 2 |
DOIs | |
State | Published - Apr 15 2019 |
All Science Journal Classification (ASJC) codes
- Modeling and Simulation
- General Engineering
- Applied Mathematics
Keywords
- Euler equations
- Inviscid limit
- Navier-Stokes equations
- Weak solutions