16 papers
Standing waves for Schrodinger equations with Kato class potentials and -bounded nonlinearities
Aleksander Ćwiszewski, Piotr Kokocki
We establish the existence of standing waves for a nonlinear Schrodinger equation with potentials belonging to the Kato class and an -bounded nonlinearity, whose Lipschit…
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…
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 (…
Well-posedness of logarithmic spiral vortex sheets
T. Cieślak, P. Kokocki, W. S. Ożański
We consider a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydro- und Aero-dynamik, 1922)…
Double spiral singularities for a flow of regular planar curves
Piotr Kokocki, Kamil Dunst
In this paper we study the singularity formation for the geometric flow of complex curves that was derived [R. E. Goldstein and D.…
On global dynamics of reaction--diffusion systems at resonance
Piotr Kokocki
In this paper we use the homotopy invariants methods to study the global dynamics of the reaction-diffusion systems that are at resonance at infinity. Considering degrees of the re…