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.).
All Science Journal Classification (ASJC) codes
- Applied Mathematics