Communications in Mathematical Sciences

Volume 20 (2022)

Number 7

On a system associated with p-wave superconductivity in $\mathbb{R}^2$

Pages: 1927 – 1949

DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n7.a6

Authors

Qinghua Chen (Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China)

Yutian Lei (Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China)

Abstract

This paper is concerned with the equations related to the p‑wave superconductivity. We find an Euler–Lagrange system of the Ginzburg–Landau free energy functional and then establish the Pohozaev identity. In addition, we estimate the uniform upper bounds of classical solutions and their gradients. Based on these results, we obtain quantization effects and asymptotic behavior at infinity of classical solutions, and the Liouville theorem of finite energy solutions.

Keywords

Ginzburg–Landau equations, p-wave superconductivity, quantization effects, finite energy solution, Liouville theorem, Pohozaev identity

2010 Mathematics Subject Classification

35Q56, 82D55

Full Text (PDF format)

The authors’ research was supported by NNSF of China (11871278).

Received 4 October 2021

Received revised 21 January 2022

Accepted 2 February 2022

Published 21 October 2022