ON THE GROWTH RATE OF SOLUTIONS TO GROSS-NEVEU AND THIRRING EQUATIONS Huh, Hyungjin;
We study the growth rate of Sobolev norm of the solutions to Gross-Neveu and Thirring equations. A well-known result is the double exponential rate. We show that the Sobolev norm grows at most an exponential rate exp().
Gross-Neveu;Thirring;Sobolev norm; bound;
G. Berkolaiko and A. Comech, On spectral stability of solitary waves of nonlinear Dirac equation in 1D, Math. Model. Nat. Phenom. 7 (2012), no. 2, 13-31.
N. Boussaid and A. Comech, On spectral stability of the nonlinear Dirac equation, arXiv:1211.3336.
T. Candy, Global existence for an $L^2$ critical nonlinear Dirac equation in one dimension, Adv. Differential Equations 16 (2011), no. 7-8, 643-666.
A. Comech, M. Guan, and S. Gustafson, On linear instability of solitary waves for the nonlinear Dirac equation, arXiv:1209.1146.
V. Delgado, Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac and other nonlinear Dirac equations in one space dimension, Proc. Amer. Math. Soc. 69 (1978), no. 2, 289-296.
R. H. Goodman, M. I. Weinstein, and P. J. Holmes, Nonlinear propagation of light in one-dimensional periodic structures, J. Nonlinear Sci. 11 (2001), no. 2, 123-168.
D. J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev. D 10 (1974), 3235-3253.
H. Huh, Global strong solution to the Thirring model in critical space, J. Math. Anal. Appl. 381 (2011), no. 2, 513-520.
H. Huh, Global solutions to Gross-Neveu equations, Lett. Math. Phys. 103 (2013), no. 8, 927-931.
D. E. Pelinovsky, Survey on global existence in the nonlinear Dirac equations in one spatial dimension, Harmonic analysis and nonlinear partial differential equations, 3750, RIMS Kokyuroku Bessatsu, B26, Kyoto, 2011.
D. E. Pelinovsky and Y. Shimabukuro, Orbital stability of Dirac solitons, Lett. Math. Phys. 104 (2014), no. 1, 21-41.
S. Selberg and A. Tesfahun, Low regularity well-posedness for some nonlinear Dirac equations in one space dimension, Differential Integral Equations 23 (2010), no. 3-4, 265-278.
Y. Zhang, Global solution to a cubic nonlinear Dirac equation in 1 + 1 dimensions, arXiv:1304.1989.