Abstract: We used the methods of conservative energy estimation and characteristic line estimation to solve the Sobolev norm growth estimation problem of the solution of the (1+1)-dimensional Maxwell-Chern-Simons-Higgs model, gave the L^∞ estimation of the first derivative of the finite energy solution of the model, and obtained the polynomial growth of the H² norm of the solution by improving the exponential growth.

Key words: Chern-Simons theory, gauge invariance, characteristic line estimation, L^∞ estimation, H² norm growth