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Weak Solutions of the Euler Equations and Onsager’s Conjecture
, M.Sc. Thesis Sharif University of Technology ; Safdari, Mohammad (Supervisor)
Abstract
The Onsager's conjecture is concerned with the dichotomy between rigidity and flexibility of weak solutions of incompressible Euler equations. Lars Onsager conjectured that weak solutions of Euler equations that are not smooth enough could be dissipative, even without the help of viscosity. On the other hand, it is well known that $C^1$ solutions conserve energy. Onsager conjectured that C^(1/3) regularity marks the threshold for this dichotomy. In other words, Hölder continuous solutions with Hölder exponent greater than 1/3 conserve the energy, while for every Hölder exponent less than 1/3, there are dissipative Hölder continuous solutions. The threshold 1/3 is intimately tied with...