A Lax pair structure for the half-wave maps equation
Sign Up to like & getrecommendations! Published in 2017 at "Letters in Mathematical Physics"
DOI: 10.1007/s11005-017-1044-x
Abstract: AbstractWe consider the half-wave maps equation $$\begin{aligned} \partial _t \vec {S} = \vec {S} \wedge |\nabla | \vec {S}, \end{aligned}$$∂tS→=S→∧|∇|S→,where $$\vec {S}= \vec {S}(t,x)$$S→=S→(t,x) takes values on the two-dimensional unit sphere $$\mathbb {S}^2$$S2 and $$x… read more here.
Keywords: maps equation; lax pair; wave maps; equation ... See more keywords
Global stability of some totally geodesic wave maps
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Differential Equations"
DOI: 10.1016/j.jde.2021.02.056
Abstract: Abstract We prove that wave maps that factor as R 1 + d → φ S R → φ I M , subject to a sign condition, are globally nonlinear stable under small compactly supported… read more here.
Keywords: global stability; wave maps; stability totally; wave ... See more keywords
Biharmonic wave maps: local wellposedness in high regularity
Sign Up to like & getrecommendations! Published in 2020 at "Nonlinearity"
DOI: 10.1088/1361-6544/ab73ce
Abstract: We show the local wellposedness of biharmonic wave maps with initial data of sufficiently high Sobolev regularity and a blow-up criterion in the sup-norm of the gradient of the solutions. In contrast to the wave… read more here.
Keywords: wave maps; local wellposedness; regularity; biharmonic wave ... See more keywords