Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Rowan Killip"'
Publikováno v:
Forum of Mathematics, Pi, Vol 12 (2024)
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ . Well-posedness has long been known for $s\geq 0$ , see [55], but not pre
Externí odkaz:
https://doaj.org/article/4f25f3788e814a4db9a2cfcca6b8648b
Publikováno v:
SIAM Journal on Mathematical Analysis. 53:5803-5812
We consider the nonlinear Schrodinger equation in three space dimensions with combined focusing cubic and defocusing quintic nonlinearity. This problem was considered previously by Killip et al. [A...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::82ca5d006d5e395636d4268887096c82
https://doi.org/10.1137/20m1381824
https://doi.org/10.1137/20m1381824
Publikováno v:
American Journal of Mathematics. 143:613-680
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::feb7726f4207867ffba2efc8262c76e9
https://doi.org/10.1353/ajm.2021.0014
https://doi.org/10.1353/ajm.2021.0014
Publikováno v:
SIAM Journal on Mathematical Analysis. 52:135-163
We consider discrete analogues of two well-known open problems regarding invariant measures for dispersive PDE, namely, the invariance of the Gibbs measure for the continuum (classical) Heisenberg ...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ca0c8e83062d23d11fd969e58ea585f0
https://doi.org/10.1137/19m1265314
https://doi.org/10.1137/19m1265314
Using the two-dimensional nonlinear Schr\"odinger equation (NLS) as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation from its small-data scattering behavior. We prove that under very mild
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b7f628f55b05e0fc00c1c905e02d09e4
Publikováno v:
Annals of PDE. 7
We prove global well-posedness of the fifth-order Korteweg-de Vries equation on the real line for initial data in $$H^{-1}(\mathbb {R})$$ . Global well-posedness in $$L^2({\mathbb {R}})$$ was shown previously in [8] using the method of commuting flow
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6b91046b729bbc9ac6f4ce2b226246e0
https://doi.org/10.1007/s40818-021-00111-4
https://doi.org/10.1007/s40818-021-00111-4
We consider the derivative NLS equation in one spatial dimension, which is known to be completely integrable. We prove that the orbits of $L^2$ bounded and equicontinuous sets of initial data remain bounded and equicontinuous, not only under this flo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43f03acd4df0dd04714bdea1913b3cf8
http://arxiv.org/abs/2106.13333
http://arxiv.org/abs/2106.13333
Publikováno v:
Revista Matemática Iberoamericana. 35:703-730
We prove inverse Strichartz theorems at L2 regularity for a family of Schrodinger evolutions in one space dimension. Prior results rely on spacetime Fourier analysis and are limited to the translation-invariant equation i∂tu=−12Δu. Motivated by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::84ebed3c9cb9ad75c9477c643e3fb8c7
https://doi.org/10.4171/rmi/1067
https://doi.org/10.4171/rmi/1067
Publikováno v:
Communications in Partial Differential Equations. 44:51-71
We prove almost sure global existence and scattering for the energy-critical nonlinear Schrodinger equation with randomized spherically symmetric initial data in Hs(R4) with 56
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16b437e9e1db0542abf35f9c34840b3b
https://doi.org/10.1080/03605302.2018.1541904
https://doi.org/10.1080/03605302.2018.1541904
We consider two discrete completely integrable evolutions: the Toda Lattice and the Ablowitz-Ladik system. The principal thrust of the paper is the development of microscopic conservation laws that witness the conservation of the perturbation determi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::627537ac26eba77c6f3f1f417368946c