Zobrazeno 1 - 10
of 12
pro vyhledávání: '"Dana Mendelson"'
Autor:
Bjoern Bringmann, Dana Mendelson
Publikováno v:
Annales Henri Poincaré. 22:3255-3290
This paper revisits the proof of Anderson localization for multi-particle systems. We introduce a multi-particle version of the eigensystem multi-scale analysis by Elgart and Klein, which had previously been used for single-particle systems.
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Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::70ca759cc2e895dba8c19bc209316733
https://doi.org/10.1007/s00023-021-01051-2
https://doi.org/10.1007/s00023-021-01051-2
Autor:
Carlos E. Kenig, Dana Mendelson
Publikováno v:
International Mathematics Research Notices. 2021:14508-14615
We consider the focusing energy-critical quintic nonlinear wave equation in 3D Euclidean space. It is known that this equation admits a one-parameter family of radial stationary solutions, called solitons, which can be viewed as a curve in $ \dot H^s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4c9c3f972e1b61d2a666995404a731b9
https://doi.org/10.1093/imrn/rnz174
https://doi.org/10.1093/imrn/rnz174
Publikováno v:
Advances in Mathematics. 347:619-676
We consider the Cauchy problem for the defocusing cubic nonlinear Schrodinger equation in four space dimensions and establish almost sure local well-posedness and conditional almost sure scattering for random initial data in H x s ( R 4 ) with 1 3 s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a70c19d9fd51b63e263cf0f12b4c98f2
https://doi.org/10.1016/j.aim.2019.02.001
https://doi.org/10.1016/j.aim.2019.02.001
Publikováno v:
Transactions of the American Mathematical Society. 371:5179-5202
We consider the cubic Gross–Pitaevskii (GP) hierarchy on R \mathbb {R} , which is an infinite hierarchy of coupled linear inhomogeneous partial differential equations appearing in the derivation of the cubic nonlinear Schrödinger equation from qua
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::47ad276b6a3a2b3d5e76ebae4bb4ea16
https://doi.org/10.1090/tran/7726
https://doi.org/10.1090/tran/7726
Publikováno v:
Anal. PDE 13, no. 7 (2020), 1995-2090
We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1+3)$-dimensions for energy subcritical powers $p$ in the range $3 < p< 5$. We prove that any solution is global-in-time and scatters to free waves in both time
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::390b381db943304f5c51f64fe6c2c5f6
https://projecteuclid.org/euclid.apde/1605754815
https://projecteuclid.org/euclid.apde/1605754815
Publikováno v:
arXiv
© 2020 Elsevier Inc. We consider the cubic nonlinear Schrödinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the knowledge that the NLS is an effective equation f
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ba71f6c40e61214be202cd9a923a1eb
https://hdl.handle.net/1721.1/136289
https://hdl.handle.net/1721.1/136289
Autor:
Dana Mendelson
Publikováno v:
Journal of Functional Analysis. 272:3019-3092
We consider the periodic defocusing cubic nonlinear Klein–Gordon equation in three dimensions in the symplectic phase space H 1 2 ( T 3 ) × H − 1 2 ( T 3 ) . This space is at the critical regularity for this equation, and in this setting there i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4ee812e91c4f9d44e2eee952ca9d0bce
https://doi.org/10.1016/j.jfa.2016.12.025
https://doi.org/10.1016/j.jfa.2016.12.025
We consider the cubic Gross-Pitaevskii (GP) hierarchy in one spatial dimension. We establish the existence of an infinite sequence of observables such that the corresponding trace functionals, which we call ``energies,'' commute with respect to the w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b33640c20441bf1ad1c06cc3fa0adfd6
Publikováno v:
arXiv
We study nonlinear wave equations on $\mathbb R^{2+1}$ with quadratic derivative nonlinearities, which include in particular nonlinearities exhibiting a null form structure, with random initial data in $H_x^1\times L^2_x$. In contrast to the countere
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::15e57141fcfe0c11ce360e60825bd957
http://arxiv.org/abs/1710.09346
http://arxiv.org/abs/1710.09346
We consider the energy-critical defocusing nonlinear wave equation on $\mathbb{R}^4$ and establish almost sure global existence and scattering for randomized radially symmetric initial data in $H^s_x(\mathbb{R}^4) \times H^{s-1}_x(\mathbb{R}^4)$ for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e41478778c8b4c15de8a868136a2b574
http://arxiv.org/abs/1703.09655
http://arxiv.org/abs/1703.09655