Equivariant wave maps in two space dimensions

By Michael Struwe. 2003

134 citations recorded by the source corpus.

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In Mathematical Physics

Citations in the corpus

Asymptotic decomposition for semilinear Wave and equivariant wave map equations (2015, methodology): “On the one hand this convergence is slightly weaker than that given by [35], (already sufficient for our purpose though) in the sense that the convergence is only for r > 0, not across origin, while on the other hand it does not require a “smallness” condition on the energy near r = 0, hence is more”
Concentration Compactness for Critical Wave Maps (2009, background): “Moreover, Struwe [50] observed that in the equivariant setting, blowup in this dimension has to result from a strictly slower than self-similar rescaling of a harmonic sphere of finite energy.”
Renormalization and blow up for charge one equivariant critical wave maps (2006, background): “lar, it is known that the latter never develop singularities [Str1], and that for equivariant wave maps of co-rotation index 1, regularity breakdown can only occur in an energy concentration scenario [Str2]. For equivariant wave maps, it is known that regularity of the initial data is preserved (see”
Regularity of Wave-Maps in Dimension 2 + 1 (2009, result): “Similar results were previously established for the Wave-Map problem via symmetry reductions in the works [4,26,30], and [29].”
Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions (2000, unknown): “Similarly, we χ −(i) j≤k = χ −(i) k≥j to denote a quantity of the form max(1, 2 δ(j−k)), where δ < Cδ 1/2 i for some absolute constant C > 0 depending only on n, and also use χ −(i) j=k to denote quantity of the form 2 δ|j−k| with the same assumptions on δ.”
On the formation of singularities in the critical $O(3)$ $\sigma$-model (2006, background): “]) and Christodoulou/Tahvildar-Zadeh (see [9]–[10]), where the context is spherical symmetry or more generally k-equivariance. There is also the important and closely related work of Struwe (see [33]–[35]), where breakdown is studied in the general (symmetric) case including maps into S2. From all t”
Soliton resolution for equivariant wave maps to the sphere (2013, methodology): “A result of this type was already obtained in [25], but only for the first scale (and in the L(2)loc(H × L(2)([0,+∞)loc) topology), i.”