On the continuity of the solution operator to the wave map system

Details On the continuity of the solution operator to the wave map system On the continuity of the solution operator to the wave map system

2002-12-15

arxiv.org/abs/math/0212194v1

Communications on Pure Applied Mathematics, 57(3), 2004, p.357 - 353

Mathematics

Analysis of PDEs

Scientific paper

We investigate the continuity properties of the solution operator to the wave
map system from the flat Minkowski space to a general nonflat target of
arbitrary dimension, and we prove by an explicit class of counterexamples that
this map is not uniformly continuous in the critical norms on any neighbourhood
of zero.

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