Small data global regularity for half-wave maps
نویسندگان
چکیده
منابع مشابه
Global Regularity and Singularity Development for Wave Maps
function space requirements: (i) X ⊂ C([0, T ],H n2 + ) ∩ C([0, T ],H n2−1+ ), > 0
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We show that wave maps from Minkowski space R to a sphere Sm−1 are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space Ḣn/2, in the high-dimensional case n ≥ 5. A major difficulty, not present in earlier results in this area, is that the Ḣn/2 norm barely fails to control L, potentially causing a logarithmic divergence in the non-linearity; however this...
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We show that wave maps from Minkowski space R to a sphere Sm−1 are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space Ḣn/2, in all dimensions n ≥ 2. This generalizes the results in the prequel [37] of this paper, which addressed the high-dimensional case n ≥ 5. In particular, in two dimensions we have global regularity whenever the energy is small, an...
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ژورنال
عنوان ژورنال: Analysis & PDE
سال: 2018
ISSN: 1948-206X,2157-5045
DOI: 10.2140/apde.2018.11.661