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We show that smooth, radially symmetric wave maps U from R2+1 to a compact target manifold N, where ∂rU and ∂tU have compact support for any fixed time, scatter. The result will follow from the work of Christodoulou ...
We prove that the blow up solutions of type II character constructed by Krieger-Schlag-Tataru [21] as well as Krieger-Schlag [20] are unstable in the energy topology in that there exist open data sets whose closure contains the dataof the preceding type II ...
We use a Leibniz-rule-type inequality for fractional derivatives to prove conditions under which a solution u(x, t) of the k-generalized KdV equation is in the space L-2(vertical bar x vertical bar(2s) dx) for s is an element of R+. ...