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)|
|Number of pages||58|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Sep 1 2016|
All Science Journal Classification (ASJC) codes
- Applied Mathematics