Global Regularity of Wave Maps from R2+1 to H2. Small Energy

By J. Krieger. 2004

78 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0c410db5c42877163fc9796c4df99c56d832b822

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In Applied Mathematics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Concentration Compactness for Critical Wave Maps (2009, methodology): “A systematic development will be carried out in Section 2 below, largely following [56] (we do need to go beyond both [56] and [22] in some instances such as by adding the sharp Strichartz spaces with the Klainerman-Tataru gain for small scales, and by eventually modifying ‖ · ‖S[k] to the stronger ”
On the formation of singularities in the critical $O(3)$ $\sigma$-model (2006, unknown): “In the case of dynamic solutions and the Cauchy problem, the only general understanding of the equations (3) that is yet available is for the local theory (see [18]) and the small data scale invariant (global) results of [37] (in the Besov case) and [36], [19], and [38] for the case of small energy.”
Renormalization and blow up for charge one equivariant critical wave maps (2006, background): “We note that a fairly satisfactory understanding has been achieved for small-energy wave maps from R 2+1 to general targets, see Tao [29], Tataru [30–32], and Krieger [ 11 ], as well as for rotationally invariant wave maps and general initial data by Christodoulou, Tahvildar-Zadeh [5], and Struwe [2”
Energy Dispersed Large Data Wave Maps in 2 + 1 Dimensions (2009, background): “There is also an extensive literature devoted to the more tractable higher dimensional case; we refer the reader to [31], [28], [8], [14], [17], and [20] for more information.”
Regularity of Wave-Maps in Dimension 2 + 1 (2009, methodology): “In the case where the target M is a negatively curved Riemann surface, Krieger and Schlag [18] provide global regularity and scattering via a modification of the Kenig-Merle method [12], which uses as a key component suitably defined BahouriGerard [1] type decompositions.”