Dissipative Euler flows with Onsager-critical spatial regularity (Q2816392)

The problem discussed in this work is connected to the so-called Onsager conjecture, which connect conditions on an existence of continuous solutions of Euler's equations, their suprema and an energy conservation, which can be established checking these solutions suprema. Thus, the authors concentrate on the relation between existence of solutions and non-conservation of the energy for a special class of weak solutions, with the main result obtained that there exists a non-trivial continuous weak solution with compact support in time on the 3-dimensional flat torus for the velocity \(v\in L^1_t(C_x^{1/3-\varepsilon})\) for any \(\varepsilon>0\). To reach this goal, the specific subdivision scheme, which constructs a triple of smooth compactly supported functions which solve the Euler-Reynolds system and checks an integer valued frequency regularity parameter has been inductively applied.