Total integrals of solutions for inhomogeneous Painlevé II equation

Speaker(s)

Piotr Kokocki

Affiliation

UMK Toruń

Date

Jan. 16, 2020, 12:30 p.m.

Room

room 5070

Seminar

Seminar of Mathematical Physics Equations Group

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We establish a formula determining the value of the Cauchy integrals for the real and purely imaginary Ablowitz-Segur solutions for the inhomogeneous second Painlevé equation. Our approach relies on the Deift-Zhou steepest descent analysis of the corresponding Riemann-Hilbert problem and the construction of an appropriate parametrix in a neighborhood of the origin. The obtained results are used to provide a rigorous proof of a numerically predicted phenomena that an arbitrary logarithmic spiral is a finite time singularity developed by a geometric flow that approximates the vortex patch dynamics of the 2D Euler equation.

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