Global Regularity of Wave Maps from R2+1 to H2. Small Energy
نویسندگان
چکیده
منابع مشابه
Global Regularity of Wave Maps from R to H. Small Energy
We demonstrate that Wave Maps with smooth initial data and small energy from R2+1 to the Lobatchevsky plane stay smooth globally in time. Our method is similar to the one employed in [18]. However, the multilinear estimates required are considerably more involved and present novel technical challenges. In particular, we shall have to work with a modification of the functional analytic framework...
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We consider Wave Maps with smooth compactly supported initial data of small Ḣ3/2-norm from R to hyperbolic 2-space and show that they stay smooth globally in time. Our methods are based on the introduction of a global Coulomb Gauge as in [13], followed by a dynamic separation as in [6]. We then rely on an adaptation of T.Tao’s methods used in his recent breakthrough result [16].
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We consider Wave Maps with smooth compactly supported initial data of small Ḣ3/2-norm from R3+1 to certain 2-dimensional Riemannian manifolds and show that they stay smooth globally in time. Our methods are based on the introduction of a global Coulomb Gauge as in [17], followed by a dynamic separation as in [8]. We then rely on an adaptation of T.Tao’s methods used in his recent breakthrough r...
متن کاملGlobal Regularity of Wave Maps Ii. Small Energy in Two Dimensions
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: Communications in Mathematical Physics
سال: 2004
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-004-1088-5