On the growth rate of solutions to Gross-Neveu and Thirring equations
Commun. Korean Math. Soc. 2014 Vol. 29, No. 2, 263-267
https://doi.org/10.4134/CKMS.2014.29.2.263
Printed April 1, 2014
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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