On the Axisymmetric Euler Equations with Initial Vorticity in Borderline Spaces of Besov Type
نویسنده
چکیده
Borderline spaces of Besov type consist of tempered distributions satisfying the property that the partial sums of their B ∞,1-norm diverge in a controlled way. We prove an existence and uniqueness result for the three-dimensional axisymmetric Euler equations without swirl when initial vorticity belongs to these spaces. We also prove that for this class of solutions the vanishing viscosity limit holds in the energy norm, and we give a rate of convergence.
منابع مشابه
The Axisymmetric Euler Equations with Vorticity in Borderline Spaces of Besov Type
Borderline spaces of Besov type consist of tempered distributions satisfying the property that the partial sums of their B ∞,1-norm diverge in a controlled way. Misha Vishik established uniqueness of solutions to the two and three-dimensional incompressible Euler equations with vorticity whose B ∞,1 partial sums diverge roughly at a rate of N logN . In two dimensions, he also established condit...
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تاریخ انتشار 2009