Schrodinger Equations: Pointwise Convergence to the Initial Data
From MaRDI portal
Publication:3800507
DOI10.2307/2047326zbMath0654.42014OpenAlexW4234350484MaRDI QIDQ3800507
Publication date: 1988
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2047326
Maximal functions, Littlewood-Paley theory (42B25) Multipliers in one variable harmonic analysis (42A45)
Related Items
Scattering for the cubic Klein–Gordon equation in two space dimensions ⋮ Optimal constants and extremisers for some smoothing estimates ⋮ On the Work of Jean Bourgain in Nonlinear Dispersive Equations ⋮ Convergence problem of reduced Ostrovsky equation in Fourier–Lebesgue spaces with rough data and random data ⋮ Uniqueness properties of solutions of Schrödinger equations ⋮ Convergence problem of Ostrovsky equation with rough data and random data ⋮ Strichartz and Local Smoothing Estimates for Stochastic Dispersive Equations with Linear Multiplicative Noise ⋮ On sharpness of the local Kato-smoothing property for dispersive wave equations ⋮ Sharp maximal estimates for doubly oscillatory integrals ⋮ Unnamed Item ⋮ Well-posedness of the cauchy problem for the long wave-short wave resonance equations ⋮ A Morawetz inequality for water waves ⋮ Smoothing effect and exponential stability of discrete-time Schrödinger equation with fractional regularization term ⋮ Convergence properties for the Schrodinger equation ⋮ A sharp Schrödinger maximal estimate in \(\mathbb{R}^2\) ⋮ Gibbs Phenomenon for Dispersive PDEs on the Line ⋮ On Kato's smoothing effect for a fractional version of the Zakharov-Kuznetsov equation ⋮ Dispersive estimates for nonhomogeneous radial phases: an application to weakly dispersive equations and water wave models ⋮ Pointwise convergence of sequential Schrödinger means ⋮ Local Smoothing Estimates for Schrödinger Equations on Hyperbolic Space ⋮ Pointwise convergence along a tangential curve for the fractional Schrödinger equation with 0 < m < 1 ⋮ Long time behavior of stochastic NLS with a small multiplicative noise ⋮ Some convergence problems regarding the fractional Schrödinger propagator on noncompact manifolds ⋮ Weighted Fourier extension estimates and applications ⋮ Strichartz and smoothing estimates for Schrödinger operators with large magnetic potentials in \(\mathbb R^3\) ⋮ Convergence problem of Schrödinger equation and wave equation in low regularity spaces ⋮ Weighted maximal estimates along curve associated with dispersive equations ⋮ A Carleson problem for the Boussinesq operator ⋮ Smoothing and Strichartz estimates for degenerate Schrödinger-type equations ⋮ Sharp pointwise convergence on the Schrödinger operator along one class of curves ⋮ Globally well and ill posedness for non-elliptic derivative Schrödinger equations with small rough data ⋮ On the Schrödinger maximal function in higher dimension ⋮ Well posedness and smoothing effect of Schrödinger-Poisson equation ⋮ Scattering for the 𝐿² supercritical point NLS ⋮ Scattering for the one-dimensional Klein–Gordon equation with exponential nonlinearity ⋮ Unnamed Item ⋮ Endpoint maximal and smoothing estimates for Schrödinger equations ⋮ Unnamed Item ⋮ Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation ⋮ A sharp 𝑘-plane Strichartz inequality for the Schrödinger equation ⋮ A Kinetic Formulation of Multidimensional Scalar Conservation Laws and Related Equations ⋮ Local smoothing for the Schrödinger equation on a multi-warped product manifold with inflection-transmission trapping ⋮ A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane ⋮ On the Generalized Benjamin-Ono Equation ⋮ On dyadic nonlocal Schrödinger equations with Besov initial data ⋮ Local smoothing effect on the Schrödinger equation with harmonic potential ⋮ Almost sure scattering for the energy-critical NLS with radial data below H1(R4) ⋮ Higher-Order Nonlinear Dispersive Equations ⋮ Some dispersive estimates for Schrödinger equations with repulsive potentials ⋮ On the defect of compactness for the Strichartz estimates of the Schrödinger equations ⋮ Strichartz and smoothing estimates for Schrödinger operators with almost critical magnetic potentials in three and higher dimensions ⋮ An improved maximal inequality for 2D fractional order Schrödinger operators ⋮ Extremizability of Fourier restriction to the paraboloid ⋮ Effective limiting absorption principles, and applications ⋮ Unnamed Item ⋮ Pointwise convergence along a tangential curve for the fractional Schrödinger equation ⋮ Global Kato type smoothing estimates via local ones for dispersive equations ⋮ Asymptotic lower bounds for a class of Schrödinger equations ⋮ Morawetz Inequalities for Water Waves ⋮ 𝐿^{𝑝}→𝐿^{{}𝑝’} estimates for time-dependent Schrödinger operators ⋮ Convergence problem of Schrödinger equation in Fourier-Lebesgue spaces with rough data and random data ⋮ Pointwise Convergence of Solutions to the Schrödinger Equation on Manifolds ⋮ Weighted Sobolev L2 estimates for a class of Fourier integral operators ⋮ On a class of solutions to the generalized derivative Schrödinger equations ⋮ Sharp \(L^2\) estimates of the Schrödinger maximal function in higher dimensions ⋮ Probabilistic pointwise convergence problem of Schrödinger equations on manifolds ⋮ Trace theorems: critical cases and best constants ⋮ On a Higher Dimensional Version of the Benjamin--Ono Equation ⋮ Dispersive blow-up and persistence properties for the Schrödinger–Korteweg–de Vries system ⋮ Kato Smoothing Effect for Schrödinger Operator ⋮ On the local smoothing for the Schrödinger equation ⋮ Maximal function estimates of solutions to general dispersive partial differential equations ⋮ Variable coefficient Schrödinger flows for ultrahyperbolic operators ⋮ A note on pointwise convergence for the Schrödinger equation ⋮ On the work of Jean Bourgain in nonlinear dispersive equations ⋮ Local Smoothing of Fourier Integral Operators and Hermite Functions ⋮ ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED LONG-SHORT WAVE EQUATIONS ⋮ Optimal forward and reverse estimates of Morawetz and Kato-Yajima type with angular smoothing index ⋮ Inégalités de résolvante pour l’opérateur de Schrödinger avec potentiel multipolaire critique ⋮ Sharp Local Smoothing Estimates for Fourier Integral Operators ⋮ A Note on the Convergence of the Schrodinger Operator along Curve ⋮ Convergence over fractals for the Schroedinger equation ⋮ Profiles for bounded solutions of dispersive equations, with applications to energy-critical wave and Schrödinger equations ⋮ A sharp scattering condition for focusing mass-subcritical nonlinear Schrödinger equation ⋮ On some Schrödinger and wave equations with time dependent potentials ⋮ Regularity, decay, and best constants for dispersive equations ⋮ Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity ⋮ The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds ⋮ Decay and regularity for dispersive equations with constant coefficients ⋮ Smoothing estimates for non-dispersive equations ⋮ The inviscid limit of the derivative complex Ginzburg-Landau equation ⋮ On nonlinear Schrödinger equations in exterior domains ⋮ Local smoothing for scattering manifolds with hyperbolic trapped sets ⋮ Smoothing effect for regularized Schrödinger equation on compact manifolds ⋮ Pointwise convergence problem of the Korteweg-de Vries-Benjamin-Ono equation ⋮ The general quasilinear ultrahyperbolic Schrödinger equation ⋮ On the dimension of the divergence set of the Ostrovsky equation ⋮ Dispersive smoothing effects for KdV type equations ⋮ Local smoothing for the quantum Liouville equation ⋮ Optimal constants of smoothing estimates for the 2D Dirac equation ⋮ Pointwise convergence over fractals for dispersive equations with homogeneous symbol ⋮ Convergence problem of the Kawahara equation on the real line ⋮ An upbound of Hausdorff's dimension of the divergence set of the fractional Schrödinger operator on \(H^s(\mathbb{R}^n)\) ⋮ Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations ⋮ Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces ⋮ On 4-order Schrödinger operator and beam operator ⋮ Uniqueness properties of higher order dispersive equations ⋮ Dimension of divergence sets for dispersive equation ⋮ Pointwise Fourier inversion: A wave equation approach ⋮ Global range estimates for maximal oscillatory integrals with radial test functions ⋮ The Kato smoothing effect for regularized Schrödinger equations in exterior domains ⋮ Sharp Morawetz estimates ⋮ Pointwise convergence of solutions to Schrödinger type equations ⋮ Nonlocal Schrödinger equations in metric measure spaces ⋮ Maximal estimate for solutions to a class of dispersive equation with radial initial value ⋮ On the dimension of divergence sets of dispersive equations ⋮ Second-order corrections to mean field evolution of weakly interacting bosons. I ⋮ Virial identity and weak dispersion for the magnetic Dirac equation ⋮ An endpoint space-time estimate for the Schrödinger equation ⋮ A sharp weighted \(L^2\)-estimate for the solution to the time-dependent Schrödinger equation ⋮ Price's law on nonstationary space-times ⋮ Averages over hypersurfaces. Smoothness of generalized Radon transforms ⋮ Global parametrices and dispersive estimates for variable coefficient wave equations ⋮ Quasilinear Schrödinger equations. I: Small data and quadratic interactions ⋮ Some remarks on localization of Schrödinger means ⋮ Space-time estimates on damped fractional wave equation ⋮ Average decay of the Fourier transform of measures with applications ⋮ Propagation of singularities and maximal functions in the plane ⋮ Local smoothing and convergence properties of Schrödinger type equations ⋮ Restriction theorems and maximal operators related to oscillatory integrals in \(\mathbf R^3\) ⋮ The Schrödinger equation along curves and the quantum harmonic oscillator ⋮ Smoothing property for the \( L^2 \)-critical high-order NLS. II ⋮ Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation ⋮ On Schrödinger oscillatory integrals associated with the Dunkl transform ⋮ On a class of solutions to the generalized derivative Schrödinger equations. II ⋮ Sharp estimates for maximal operators associated to the wave equation ⋮ A study on a class of generalized Schrödinger operators ⋮ Space-time estimates for the wave equations with singular potentials ⋮ Maximal functions associated with nonisotropic dilations of hypersurfaces in \(\mathbb R^3\) ⋮ A local smoothing estimate for the Schrödinger equation ⋮ Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations ⋮ Approximation of the fractional Schrödinger propagator on compact manifolds ⋮ Coherence on fractals versus pointwise convergence for the Schrödinger equation ⋮ Small solutions to nonlinear Schrödinger equations ⋮ Regularity of the Schrödinger equation for the harmonic oscillator ⋮ Problems on pointwise convergence of solutions to the Schrödinger equation ⋮ Convergence of solutions of general dispersive equations along curve ⋮ Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary ⋮ On pointwise convergence for Schrödinger operator in a convex domain ⋮ Convergence of sequences of Schrödinger means ⋮ Endpoint Strichartz estimates for the magnetic Schrödinger equation ⋮ The Cauchy problem for quasi-linear Schrödinger equations ⋮ Estimates for multiparameter maximal operators of Schrödinger type ⋮ Dimension of divergence sets for the pointwise convergence of the Schrödinger equation ⋮ The quantum hydrodynamics system in two space dimensions ⋮ Spectral identities and smoothing estimates for evolution operators ⋮ On the finite energy weak solutions to a system in quantum fluid dynamics ⋮ Strichartz estimates via the Schrödinger maximal operator ⋮ Local smoothing effects for the water-wave problem with surface tension ⋮ A remark on Schrödinger operators ⋮ Dispersive blow-up for nonlinear Schrödinger equations revisited ⋮ A note on non-tangential convergence for Schrödinger operators ⋮ Local regularity of solutions to wave equations with time-dependent potentials ⋮ Smoothing effect for time-degenerate Schrödinger operators ⋮ Magnetic virial identities, weak dispersion and Strichartz inequalities ⋮ Regularity and decay of solutions to the Stark evolution equation ⋮ Smoothing estimates for the Schrödinger equation with unbounded potentials ⋮ Global maximal inequality to a class of oscillatory integrals ⋮ Quasilinear Schrödinger equations. III: Large data and short time. ⋮ \(L^p\)-estimate of Schrödinger maximal function in higher dimensions ⋮ A smoothing property for the \(L^2\)-critical NLS equations and an application to blowup theory ⋮ A Morawetz inequality for gravity-capillary water waves at low bond number ⋮ Orbital stability of solitary waves for the generalized long-short wave resonance equations with a cubic-quintic strong nonlinear term ⋮ Asymptotics for the time dependent Ginzburg-Landau equations ⋮ Pointwise convergence of the fractional Schrödinger equation in \(\mathbb{R}^2\) ⋮ Maximal Schrödinger operators with complex time ⋮ Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data ⋮ Pointwise convergence along restricted directions for the fractional Schrödinger equation ⋮ Dispersion and moment lemmas revisited ⋮ Maximal estimates for Weyl sums on \(\mathbb{T}^d\) (with an appendix by Alex Barron) ⋮ Convergence over fractals for the periodic Schrödinger equation ⋮ On the Davey-Stewartson systems ⋮ Weighted estimates for a class of global maximal operators associated with dispersive equation ⋮ Global \(L^{2}\) estimates for a class of maximal operators associated to general dispersive equations
This page was built for publication: Schrodinger Equations: Pointwise Convergence to the Initial Data
