Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2014; 29(2): 263-267

Printed April 1, 2014

https://doi.org/10.4134/CKMS.2014.29.2.263

Copyright © The Korean Mathematical Society.

On the growth rate of solutions to Gross-Neveu and Thirring equations

Hyungjin Huh

Chung-Ang University

Abstract

We study the growth rate of $H^1$ Sobolev norm of the solutions to Gross-Neveu and Thirring equations. A well-known result is the double exponential rate. We show that the $H^1$ Sobolev norm grows at most an exponential rate $\exp(c\, t^2)$.

Keywords: Gross-Neveu, Thirring, Sobolev norm, $L^{\infty}$ bound

MSC numbers: 35L45, 35Q41, 35F25, 81Q05

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