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Journal of functional analysis, ISSN 0022-1236, 2008, Volume 255, Issue 6, pp. 1497 - 1553
In this article we study global-in-time Strichartz estimates for the Schrödinger evolution corresponding to long-range perturbations of the Euclidean Laplacian... 
Strichartz estimates | Asymptotically flat | Schrödinger equation | Local smoothing | asymptotically flat | local smoothing | MATHEMATICS | Schrodinger equation | NONSMOOTH COEFFICIENTS | SINGULARITIES | INEQUALITY | OPERATORS
Journal Article
Journal of functional analysis, ISSN 0022-1236, 2018, Volume 274, Issue 2, pp. 605 - 658
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 02/2017, Volume 150, pp. 61 - 75
We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth conditions. In R3... 
Wave equation | Strichartz estimate | General measure | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON EQUATION | KAKEYA CONJECTURES | DECAY | DISTANCE SETS | FOURIER-TRANSFORMS | MATHEMATICS | DIMENSION | RESTRICTION ESTIMATE | SCATTERING | BILINEAR APPROACH
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 1, pp. 236 - 248
In this paper we study the Strichartz estimates for the Schrödinger propagator in the context of Wiener amalgam spaces which, unlike the Lebesgue spaces, control the local regularity of a function and its decay at infinity separately... 
Schrödinger propagator | Wiener amalgam spaces | Strichartz estimates | MATHEMATICS | Schrodinger propagator | MATHEMATICS, APPLIED | DECAY
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 2017, Volume 37, Issue 6, pp. 3387 - 3410
We prove new inhomogeneous generalized Strichartz estimates, which do not follow from the homogeneous generalized estimates by virtue of the Christ-Kiselev lemma... 
Spherical symmetry | Strichartz estimates | Spherical averages | Dispersive equations | Inhomogeneous equations | SCHRODINGER-EQUATIONS | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | spherical symmetry | DECAY | spherical averages | inhomogeneous equations | Mathematics - Analysis of PDEs
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2018, Volume 265, Issue 11, pp. 5656 - 5675
We consider the Lt2Lxr estimates for the solutions to the wave and Schrödinger equations in high dimensions... 
Strichartz estimates | Nonlinear wave equation | Nonlinear Schrödinger equation | MATHEMATICS | DECAY | Nonlinear Schrodinger equation | SCATTERING
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2016, Volume 442, Issue 2, pp. 715 - 725
Foschi and Vilela in their independent works [3,13] showed that the range of (1/r,1/r˜) for which the inhomogeneous Strichartz estimate... 
Schrödinger equation | Strichartz estimates | MATHEMATICS | MATHEMATICS, APPLIED | Schrodinger equation | DECAY | WAVE-EQUATIONS
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 11/2017, Volume 273, Issue 9, pp. 2846 - 2869
We prove Strichartz estimates over large time scales for the Schrödinger equation set on irrational tori... 
Linear Schrodinger equation | Strichartz estimates | Irrational tori | MATHEMATICS | INEQUALITIES | SURFACES
Journal Article
The Journal of Geometric Analysis, ISSN 1050-6926, 7/2019, Volume 29, Issue 3, pp. 2957 - 2984
.... We establish the global-in-time Strichartz estimate for Klein–Gordon equation without loss of derivative by using the microlocalized spectral measure of Laplacian... 
Scattering manifold | 35S30 | Mathematics | 35Q40 | Scattering theory | Abstract Harmonic Analysis | Strichartz estimate | Fourier Analysis | Spectral measure | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Global existence | Differential Geometry | Dynamical Systems and Ergodic Theory | 47J35 | EXISTENCE | PARAMETRIX | SITTER | MATHEMATICS | REGULARITY | RESOLVENT | WAVE-EQUATIONS | OPERATORS | PROPAGATOR
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 1/2013, Volume 62, Issue 3, pp. 991 - 1020
In this paper, we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to the spaces of Sobolev... 
Preliminary estimates | Interpolation | Cauchy Schwarz inequality | Spherical harmonics | Wave equations | Dyadics | Orthogonality | Bessel functions | Spherical coordinates | Angular regularity | Strichartz estimates | Dispersive equations | MATHEMATICS | angular regularity | SCHRODINGER-EQUATION | CONVERGENCE | WAVE-EQUATION | dispersive equations | OPERATORS | CURVES
Journal Article
by Hong, Y and Yang, C
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, ISSN 1078-0947, 06/2019, Volume 39, Issue 6, pp. 3239 - 3264
In this paper, we investigate Strichartz estimates for discrete linear Schrodinger and discrete linear Klein-Gordon equations on a lattice hZ(d) with h... 
MATHEMATICS, APPLIED | Strichartz estimates | well-posedness | DISCRETE NONLINEAR SCHRODINGER | discrete Klein-Gordon equation | DISPERSIVE PROPERTIES | MATHEMATICS | harmonic analysis on lattice | SOLITONS | Discrete Schrodinger equation | CONVERGENCE | WAVE-GUIDE ARRAYS | EQUATION | SCHEMES
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7293 - 7333
...-square type potentials and includes several anisotropic potentials. We first prove weighted resolvent estimates, which are uniform with respect to the energy, with a large class of weight functions in Morrey-Campanato spaces... 
Resolvent estimates | Strichartz estimates | Critical singularities | Schrödinger operator | MAGNETIC POTENTIALS | INEQUALITIES | PERTURBATIONS | critical singularities | CRITICAL DECAY | resolvent estimates | L-P | MATHEMATICS | DIMENSIONS | WEAKLY CONJUGATE OPERATOR | ENERGY ASYMPTOTICS | TIME-DECAY | Schrodinger operator | WAVE-EQUATION
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 10/2017, Volume 263, Issue 7, pp. 3832 - 3853
The purpose of this paper is to study the validity of global-in-time Strichartz estimates... 
Schrödinger equation | Strichartz estimates | Inverse-square potential | MAGNETIC POTENTIALS | MATHEMATICS | Schrodinger equation | INEQUALITIES | CUBIC NLS | TIME DECAY | WAVE-EQUATION | OPERATORS
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 03/2015, Volume 32, Issue 2, pp. 347 - 371
...(R2) for s>12 and globally well-posed in H1(R×T) and in Hs(R3) for s>1. Our main new ingredient is a bilinear Strichartz estimate in the context of Bourgain's... 
Bourgain's spaces | Zakharov–Kuznetsov equation | Initial value problem | Well-posedness | Bilinear Strichartz estimates | Zakharov-Kuznetsov equation | MATHEMATICS, APPLIED | TRANSVERSE NONLINEAR INSTABILITY | CAUCHY-PROBLEM | RESTRICTION | SCATTERING
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 6871 - 6907
.... Our work is directly related to the study of extremizers and optimal constants for Strichartz estimates of certain higher order Schrodinger equations... 
Fourier extension theory | Strichartz inequalities | Extremizers | Concentration-compactness | Convolution of singular measures | Optimal constants | EXISTENCE | MATHEMATICS | optimal constants | MAXIMIZERS | convolution of singular measures | INEQUALITY | extremizers | concentration-compactness | EXTREMALS | TRANSFORMS
Journal Article
International mathematics research notices, ISSN 1687-0247, 2014, Volume 2014, Issue 5, pp. 1367 - 1378
We prove a sharp bilinear estimate for the one-dimensional Klein-Gordon equation... 
EXISTENCE | MATHEMATICS | STRICHARTZ INEQUALITIES | MAXIMIZERS | DECAY | CONE | TRANSFORMS
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2016, Volume 271, Issue 8, pp. 2339 - 2358
We prove local smoothing estimates for the massless Dirac equation with a Coulomb potential in 2 and 3 dimensions... 
Dispersive PDEs | Dirac equation | Smoothing estimates | SCHRODINGER-EQUATIONS | MATHEMATICS | STRICHARTZ | WAVE | DECAY | POTENTIALS | SMALL INITIAL DATA | OPERATORS | SELF-ADJOINT EXTENSIONS | Mathematical Physics | Analysis of PDEs | Mathematics
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 12/2017, Volume 42, Issue 12, pp. 1962 - 1981
We study the global-in-time Strichartz estimates for the Schrödinger equation on a class of scattering manifolds X ∘ . Let where Δ... 
scattering manifold | Strichartz estimate | resolvent estimate | Mild trapped set | MATHEMATICS, APPLIED | DECAY | POTENTIALS | 35Q40 | MATHEMATICS | ASYMPTOTICALLY CONIC MANIFOLDS | WAVE-EQUATION | 42B37 | SEMICLASSICAL RESOLVENT | TRAPPED SETS | 47J35 | Operators (mathematics) | Scattering | Schroedinger equation
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 2016, Volume 368, Issue 12, pp. 8755 - 8784
.... The key point of our work is to make a direct link between the problem and the weighted L-2 resolvent estimates parallel to(-Delta-z)(-1)f parallel to(L2... 
Resolvent estimates | Unique continuation | Schrödinger equations | MATHEMATICS | STRICHARTZ | Schrodinger equations | INEQUALITIES | DECAY | unique continuation
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 258, Issue 10, pp. 3227 - 3240
We prove Strichartz estimates for the Schrödinger equation with an electromagnetic potential, in dimension n ⩾ 3... 
Strichartz estimates | Schrödinger equation | Dispersive equations | Magnetic potential | MATHEMATICS | WAVE | ROUGH | Schrodinger equation | DECAY | POTENTIALS | OPERATORS | Electromagnetism
Journal Article
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