Radially symmetric wave maps from (1 + 2)-dimensional Minkowski space to the sphere

By Michael Struwe. 2002

47 citations recorded by the source corpus.

Subfields: Astronomy and Astrophysics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/988acd7b3e291c7c19415e27d311bc6b47033e58

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In Astronomy and Astrophysics

In Ocean Engineering

Citations in the corpus

On the formation of singularities in the critical $O(3)$ $\sigma$-model (2006, background): “he asymptotics (22) modulo O(c 1 2 0 ). 1.2. The family of static solutions and a modulational version of Theorem 1.3. As we have mentioned previously, it is well known from work of Struwe (see again [33]) that any blowup of the form described in Theorem 1.3 must in fact be a “bubbling oﬀ” of a stat”
Classification of radial solutions of the focusing, energy-critical wave equation (2012, background): “In the finite time blow-up case, there are some large data results for critical equivariant wave-maps into the sphere due to Christodoulou -Tahvildar-Zadeh, Shatah Tahvildar-Zadeh and Struwe (see [8, 43, 45]) which show convergence along some sequence of times, locally to a soliton (harmonic map).”
Universality of blow-up profile for small radial type II blow-up solutions of energy-critical wave equation (2009, background): “See also the article of Shatah and Tahvildar-Zadeh [STZ97] which established a result similar to Theorem 2 in this context, the articles of Struwe [ Str02 , Str03], and the recent preprint of Sterbenz and Tataru [ST09] for the general case of solutions without any special invariant properties.”
Equivariant wave maps in two space dimensions (2003, result): “Similar results also hold true in the case of radially symmetric wave maps U = U (t, r) from R1+2 to a sphere [6].”
Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions (2000, result): “us reduced to demonstrating the non-concentration of energy. This non-concentration is known if one assumes some symmetry on the data and some curvature assumptions on the target manifold ([3], [27], [31], [32]), but is not known in general. For further discussion on these problems see, e.g. [14], [”