有限能量Chern-Simons-Higgs方程的整体适定性
Global well-posedness of the Chern-Simons-Higgs equations with finite energy
摘要：
本文证明了（2+1）维Minkowski时空上Chern-Simons-Higgs方程的Cauchy问题对于有限能量的初值是整体适定的.这改进了Chae和Choe的结果，他们证明了更规则数据的全局适定性。利用Lorenz规范下系统的零结构和波-Sobolev范数的双线性时空估计，证明了系统在能量正则性下的局部适定性.
英文摘要：
We prove that the Cauchy problem for the Chern-Simons-Higgs equations on the (2+1)-dimensional Minkowski space-time is globally well posed for initial data with finite energy. This improves a result of Chae and Choe, who proved global well-posedness for more regular data. Moreover, we prove local well-posedness even below the energy regularity, using the the null structure of the system in Lorenz gauge and bilinear space-time estimates for wave-Sobolev norms.
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