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math.AP2023
Standing Waves for Schrödinger Equations with Kato-Rellich potentials
Aleksander Ćwiszewski, Piotr Kokocki
We show the existence of standing waves for the nonlinear Schrödinger equation with Kato-Rellich type potential. We consider both resonant with the nonlinearity satisfying one of L…
math.AP2023
Linear instability of symmetric logarithmic spiral vortex sheets
Tomasz Cieślak, Piotr Kokocki, Wojciech S. Ożański
We consider Alexander spirals with branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the (…