Semilinear Schrodinger Equations

By T. Cazenave. 2003

2,870 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3f1d7d89eb306ff4b04fe868fc3dfa593c6c933d

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In Mathematical Physics

Citations in the corpus

On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations (2006, neutral): “Let H(t) = x + 2it∇ be the Galilean operator, it has been shown in [6] that H(t) = U(t)xU(−t) = 2ite i|x| 2 4t ∇x ( e− i|x|2 4t ·), ∀t > 0,”
Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, methodology): “7) follows from the classical arguments [73,173].”
On sharp Strichartz inequalities in low dimensions (2006, methodology): “Later simplified proofs were given by Ginibre and Velo [4], see also [2, 11].”
Almost global wellposedness of the 2-D full water wave problem (2009, neutral): “We know the invariant vector fields for ∂2 t − i∂α(10) are consisting of (see [4, 35]) ∂t , ∂α, L0 = 1 2 t∂t + α∂α and 0 = α∂t + 1 2 t i (3.”
Existence and Stability of the log–log Blow-up Dynamics for the L2-Critical Nonlinear Schrödinger Equation in a Domain (2007, result): “In dimension N = 1, 2 and for any domain Ω, it was obtained in [26]; see [7] for further references and a theorem including all previous results.”
Strichartz estimates for long range perturbations (2005, background): “4) (see [15, 20, 9, 14]) that one has the following global well-posedness result for (7.”
Global Solutions for 3D Quadratic Schrödinger Equations (2008, background): “We will review results concerning global existence and asymptotic behavior for small solutions.”
MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS (2013, background): “In this case, global smooth solutions disperse and in many cases even scatter to a linear state (possibly after modulation by a real phase when d = 1, p = 3) [28, 30, 33, 35, 36, 55, 69, 70, 76, 81, 89, 91].”
Long‐Time Asymptotics for the Focusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions at Infinity and Asymptotic Stage of Modulational Instability (2015, background): “[18] T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics 10, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003.”
On collapsing ring blow up solutions to the mass supercritical NLS (2012, background): “own on blow up is the existence of a universal upper bound on blow up rate1 ZT 0 (T−t)k∇u(t)k2 L2dt<+∞ (1.8) which is a direct consequence of the time integration of the virial identity (1.4), see [4]. In [28], Merle and Raphaël consider radial data in the range 0 <sc <1, and 1for data u 0 ”