Decay estimates and Strichartz estimates of fourth-order Schrödinger operator
DOI10.1016/j.jfa.2017.10.014zbMath1379.58013arXiv1703.00295OpenAlexW2962710227MaRDI QIDQ1677466
Avy Soffer, Hong Liang Feng, Xiao Hua Yao
Publication date: 21 November 2017
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1703.00295
Strichartz estimatefourth-order Schrödinger operatorJensen-Kato dispersion decay estimateLS-pointwise decay estimate
Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Multipliers for harmonic analysis in several variables (42B15) General theory of partial differential operators (47F05)
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- Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrödinger type equation on torus
- Regularity of eigenstates in regular Mourre theory
- Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions \(d\geqslant 9\)
- Commutators, \(C_{0}\)-semigroups and resolvent estimates
- Abstract theory of pointwise decay with applications to wave and Schrödinger equations
- Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces
- Carleman estimates and absence of embedded eigenvalues
- Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces
- Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
- Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation
- Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians
- Global well-posedness and scattering for the focusing energy-critical nonlinear Schrödinger equations of fourth order in the radial case
- High energy resolvent estimates. I: First order operators
- A new proof of the Mourre estimate
- High energy resolvent estimates. II: Higher order elliptic operators
- Spectral properties of Schrödinger operators and time-decay of the wave functions. Results in \(L^ 2(R^ 4)\)
- Unique continuation and absence of positive eigenvalues for Schrödinger operators. (With an appendix by E. M. Stein)
- Existence of solutions for Schrödinger evolution equations
- Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators
- Nonlinear oscillations in a suspension bridge
- Spectral properties of Schrödinger operators and time-decay of the wave functions results in \(L^2(\mathbb{R}^m),\;m\geq 5\)
- Spectral properties of Schrödinger operators and time-decay of the wave functions
- Absence of singular continuous spectrum for certain self-adjoint operators
- Asymptotic expansions in time for solutions of Schrödinger-type equations
- Decay estimates for fourth order wave equations
- Stability and instability of fourth-order solitary waves
- On the absence of positive eigenvalues of Schrödinger operators with rough potentials
- Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
- Time decay for the nonlinear beam equation
- Exponential bounds and absence of positive eigenvalues for N-body Schrödinger operators
- On the absence of positive eigenvalues for one-body Schrödinger operators
- The analysis of linear partial differential operators. II: Differential operators with constant coefficients
- Solitons of the fourth order nonlinear Schrödinger equation
- Gaussian bounds for higher-order elliptic differential operators with Kato type potentials
- Scattering and the Levandosky-Strauss conjecture for fourth-order nonlinear wave equations
- Wellposedness for the fourth order nonlinear Schrödinger equations
- Dispersive estimates for Schrödinger operators in dimension two
- Dispersion Decay and Scattering Theory
- Growth properties of solutions of the reduced wave equation with a variable coefficient
- Travelling Waves in a Suspension Bridge
- The limiting absorption principle for partial differential operators
- Decay estimates for Schrödinger operators
- Endpoint Strichartz estimates
- A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS
- Spherically Averaged Endpoint Strichartz Estimates For The TwoDimensional Schrödinger Equation
- ERRATUM: A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS
- Dispersion estimates for fourth order Schrödinger equations
- Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
- Dispersive Estimates with Geometry of Finite Type
- \(C_0\)-groups, commutator methods and spectral theory of \(N\)-body Hamiltonians
- On the virial theorem in quantum mechanics