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Title:
Toward numerical implementation of the construction of dissipative Euler solutions with the Mikado flow
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Abstract:
Buckmaster, De Lellis, Szekelyhidi and Vicol updated recently a mathematical construction of weak solutions of the Euler equation with a prescribed energy as a function of time (arXiv:1701.08678). Moreover as well as the energy we can control the Holder exponent of the solution, which can be arbitrary close to 1/3. In the construction, so-called Mikado flow (a set of slender jets) plays an important role. We see a great potential of the solutions for a test tube of turbulence problem. Some of the quantities of interest are not easy to evaluate mathematically. Hence its numerical implementation of their method is needed. We present our ongoing work on translating their mathematical construction into a numerical simulation.
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