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pro vyhledávání: '"Mendelson, Dana"'
Autor:
Fan, Chenjie, Mendelson, Dana
In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schr\"odinger equation on $\mathbb{R}^{2}$ under rough but structured random perturbations at $L^{2}(\mathbb{R}^2)$ regularity. In particular, by employing probabil
Externí odkaz:
http://arxiv.org/abs/2010.07821
Autor:
Bringmann, Bjoern, Mendelson, Dana
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:
http://arxiv.org/abs/2010.03669
Autor:
Engelstein, Max, Mendelson, Dana
Publikováno v:
Ars Inveniendi Analytica (2022), Paper No. 5, 30 pp
We consider wave maps from $\mathbb R^{2+1}$ to a $C^\infty$-smooth Riemannian manifold, $\mathcal N$. Such maps can exhibit energy concentration, and at points of concentration, it is known that the map (suitably rescaled and translated) converges w
Externí odkaz:
http://arxiv.org/abs/2005.14128
Autor:
Mendelson, Dana, Nahmod, Andrea R., Pavlović, Nataša, Rosenzweig, Matthew, Staffilani, Gigliola
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:
http://arxiv.org/abs/1910.06959
Autor:
Mendelson, Dana, Nahmod, Andrea R., Pavlović, Nataša, Rosenzweig, Matthew, Staffilani, Gigliola
We consider the cubic nonlinear Schr\"odinger 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 for a system of intera
Externí odkaz:
http://arxiv.org/abs/1908.03847
Autor:
Kenig, Carlos, Mendelson, Dana
We consider the focusing energy-critical quintic nonlinear wave equation in three dimensional 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 curv
Externí odkaz:
http://arxiv.org/abs/1903.07246
Publikováno v:
Analysis & PDE 13 (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:
http://arxiv.org/abs/1810.03182
We consider the Cauchy problem for the defocusing cubic nonlinear Schr\"odinger equation in four space dimensions and establish almost sure local well-posedness and conditional almost sure scattering for random initial data in $H^s_x(\mathbb{R}^4)$ w
Externí odkaz:
http://arxiv.org/abs/1802.03795
Autor:
Mendelson, Dana, Nahmod, Andrea R., Pavlović, Nataša, Rosenzweig, Matthew, Staffilani, Gigliola
Publikováno v:
In Advances in Mathematics 17 September 2022 406
Autor:
Mendelson, Dana Sydney
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 133-137).
In the first part of this thesis we consider the defocus
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 133-137).
In the first part of this thesis we consider the defocus
Externí odkaz:
http://hdl.handle.net/1721.1/99324