Global existence and uniqueness of Schrödinger maps in dimensions d... 4
By I. Bejenaru, A. Ionescu, Carlos E. Kenig. 2007
78 citations recorded by the source corpus.
Abstract In dimensions d ⩾ 4 , we prove that the Schrodinger map initial-value problem { ∂ t s = s × Δ s on R d × R ; s ( 0 ) = s 0 admits a unique solution s : R d × R → S 2 ↪ R 3 , s ∈ C ( R : H Q ∞ ) , provided that s 0 ∈ H Q ∞ and ‖ s 0 − Q ‖ H ˙ d / 2 ≪ 1 , where Q ∈ S 2 .
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ec6aaca3acd81e398d60ef1b08718fc69a0ac6a3
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In Applied Mathematics
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Global Solvability of the Cauchy Problem for the Landau-Lifshitz-Gilbert Equation in Higher Dimensions (2011, methodology): “Whereas a priori estimates for Schödinger maps mainly rely on sophisticated Paley-Littlewood decompositions and Strichartz estimates for dispersive equation, see [3, 4], a priori estimates for LLG will rest on methods from semilinear parabolic systems and in particular the usage of weighted-in-time ”
- Global Schrödinger maps in dimensions $d≥ 2$: Small data in the critical Sobolev spaces (2011, methodology): “This choice works well in high dimension d ≥ 4; see [3].”