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

초록

By making use of local energy conservation, we estimate the L∞ norm of the first derivative of the solution to the Maxwell-gauged O(3) sigma model in R1+1. As an application of the bound, we obtain the growth of the H2 norm of the solution. Quadratic polynomial growth is obtained by improving exponential growth. A similar idea can be applied to the Maxwell–Klein–Gordon equations in R1+1. © 2020 Elsevier Inc.

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