Abstract
For any ɛ > 0 we show the existence of continuous periodic weak solutions v of the Euler equations that do not conserve the kinetic energy and belong to the space (Formula presented.) ; namely, x ↦ v (x,t) is ⅓−ε-Hölder continuous in space at a.e. time t and the integral (Formula presented.) is finite. A well-known open conjecture of L. Onsager claims that such solutions exist even in the class (Formula presented.).
Original language | English (US) |
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Pages (from-to) | 1613-1670 |
Number of pages | 58 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 69 |
Issue number | 9 |
DOIs | |
State | Published - Sep 1 2016 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics