On the Flow Map for 2d Euler Equations with Unbounded Vorticity
نویسندگان
چکیده
In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Hölder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.
منابع مشابه
Lack of Hölder Regularity of the Flow for 2d Euler Equations with Unbounded Vorticity
We construct a class of examples of initial vorticities for which the solution to the Euler equations in the plane has an associated flow that lies in no Hölder space of positive exponent for any positive time. Our initial vorticities have L-norms that do not grow much faster than log p, which Yudovich showed ensures the uniqueness of solutions to the Euler equations ([8]). Our class of example...
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