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Autor:
Khalil, Karim R. Shikh
It is known from the work of Koch that the two-dimensional incompressible Euler equations propagate Dini modulus of continuity for the vorticity. In this work, we consider the two-dimensional Euler equations with a modulus of continuity for vorticity
Externí odkaz:
http://arxiv.org/abs/2408.13956
We prove strong ill-posedness in $L^{\infty}$ for linear perturbations of the 2d Euler equations of the form: \[\partial_t \omega + u\cdot\nabla\omega = R(\omega),\] where $R$ is any non-trivial second order Riesz transform. Namely, we prove that the
Externí odkaz:
http://arxiv.org/abs/2207.04556