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We study the growth rate of H 1 Sobolev norm of the solu- tions 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(ct 2 ). uW(u, v), i(@tv − @xv) + mu = @¯ vW(u, v), u(x,0) = u0(x), v(x,0) = v0(x),

ON THE GROWTH RATE OF SOLUTIONS TO GROSS-NEVEU AND THIRRING EQUATIONS