Orbital stability vs. scattering in the cubic-quintic Schrödinger equation
We consider the cubic-quintic nonlinear Schrödinger equation of up to three space
dimensions. The cubic nonlinearity is thereby focusing while the quintic one is defocusing …
dimensions. The cubic nonlinearity is thereby focusing while the quintic one is defocusing …
Scattering for the non-radial 3D cubic nonlinear Schrödinger equation
Scattering of radial $ H^ 1$ solutions to the 3D focusing cubic nonlinear Schr\" odinger
equation below a mass-energy threshold $ M [u] E [u]< M [Q] E [Q] $ and satisfying an initial …
equation below a mass-energy threshold $ M [u] E [u]< M [Q] E [Q] $ and satisfying an initial …
A new proof of scattering below the ground state for the 3D radial focusing cubic NLS
B Dodson, J Murphy - Proceedings of the American Mathematical Society, 2017 - ams.org
We revisit the scattering result of Holmer and Roudenko (2008) on the radial focusing cubic
NLS in three space dimensions. Using the radial Sobolev embedding and a virial/Morawetz …
NLS in three space dimensions. Using the radial Sobolev embedding and a virial/Morawetz …
The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
We consider the focusing energy-critical nonlinear Schr\" odinger equation $ iu_t+\Delta u=-|
u|^{4\over {d-2}} u $ in dimensions $ d\geq 5$. We prove that if a maximal-lifespan solution …
u|^{4\over {d-2}} u $ in dimensions $ d\geq 5$. We prove that if a maximal-lifespan solution …
[图书][B] Structure and randomness: pages from year one of a mathematical blog
T Tao - 2008 - books.google.com
" There are many bits and pieces of folklore in mathematics that are passed down from
advisor to student, or from collaborator to collaborator, but which are too fuzzy and non …
advisor to student, or from collaborator to collaborator, but which are too fuzzy and non …
Global well-posedness and blow-up on the energy space for the Inhomogeneous Nonlinear Schr\" odinger Equation
LG Farah - arXiv preprint arXiv:1610.06901, 2016 - arxiv.org
We consider the supercritical inhomogeneous nonlinear Schr\" odinger equation (INLS) $$
i\partial_t u+\Delta u+| x|^{-b}| u|^{2\sigma} u= 0, $$ where $(2-b)/N<\sigma<(2-b)/(N-2) …
i\partial_t u+\Delta u+| x|^{-b}| u|^{2\sigma} u= 0, $$ where $(2-b)/N<\sigma<(2-b)/(N-2) …
[图书][B] Invariant manifolds and dispersive Hamiltonian evolution equations
K Nakanishi, W Schlag - 2011 - books.google.com
The notion of an invariant manifold arises naturally in the asymptotic stability analysis of
stationary or standing wave solutions of unstable dispersive Hamiltonian evolution …
stationary or standing wave solutions of unstable dispersive Hamiltonian evolution …
On well posedness for the inhomogeneous nonlinear Schrödinger equation
CM Guzmán - Nonlinear Analysis: Real World Applications, 2017 - Elsevier
The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the
inhomogeneous nonlinear Schrödinger equation (INLS) iu t+ Δ u+ λ| x|− b| u| α u= 0, where …
inhomogeneous nonlinear Schrödinger equation (INLS) iu t+ Δ u+ λ| x|− b| u| α u= 0, where …
The focusing cubic NLS with inverse-square potential in three space dimensions
We consider the focusing cubic nonlinear Schrödinger equation with inverse-square
potential in three space dimensions. We identify a sharp threshold between scattering and …
potential in three space dimensions. We identify a sharp threshold between scattering and …
Scattering for the focusing energy-subcritical nonlinear Schrödinger equation
DY Fang, J Xie, T Cazenave - Science China Mathematics, 2011 - Springer
For the 3D focusing cubic nonlinear Schrödinger equation, scattering of H 1 solutions inside
the (scale invariant) potential well was established by Holmer and Roudenko (radial case) …
the (scale invariant) potential well was established by Holmer and Roudenko (radial case) …