L∞ bounds for Chern-Simons gauged equations in R1+1 and their applications

We estimate the L-infinity norm of the first derivative of the solution to the Chern-Simons gauged O(3) sigma model in R1+1 by using local energy conservation and observing the transport equation along the characteristic line. As an application of the bound, we improve the growth rate of the H-2 norm of the solution from an exponential to a polynomial one. We also apply a similar idea to the Chern-Simons-Higgs model. Published under license by AIP Publishing.