Related papers: Weighted decay for magnetic Schroedinger equation
In this paper, we address the space-time decay properties for strong solutions to the incompressible viscous resistive Hall-MHD equations. We obtained the same space-time decay rates as those of the heat equation. Based on the temporal…
We consider a class of linear Schroedinger equations in R^d, with analytic symbols. We prove a global-in-time integral representation for the corresponding propagator as a generalized Gabor multiplier with a window analytic and decaying…
We build a smooth time-dependent real potential on the two-dimensional torus, decaying as time tends to infinity in Sobolev norms along with all its time derivative, and we exhibit a smooth solution to the associated Schr\"odinger equation…
We study the defocusing energy-critical inhomogeneous nonlinear Schr\"odinger equation \[ i\partial_tu+\Delta u=|x|^{-b}|u|^{\frac{4-2b}{d-2}}u, \qquad (t,x)\in\R\times\R^d, \] with initial data $u_0\in\dot H_x^1(\R^d)$, where $d\ge 3$ and…
The exact solution of N- dimensional radial Schr\"odinger equation with the generalized Cornell potential has been obtained using the Laplace transformation (LT) method. The energy eigenvalues and the corresponding wave functions for any…
We prove pointwise in time decay estimates via an abstract conjugate operator method. This is then applied to a large class of dispersive equations.
We provide a unified viewpoint on two illposedness mechanisms for dispersive equations in one spatial dimension, namely degenerate dispersion and (the failure of) the Takeuchi--Mizohata condition. Our approach is based on a robust energy-…
We prove the local energy decay and the smoothing effect for the damped Schr{\"o}dinger equation on R^d. The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform…
We present a solitary wave solution of the generalized nonlinear Schrodinger equation for dispersive permittivity and permeability using a scaling transformation and coupled amplitude-phase formulation. We have considered the third-order…
In this paper we develop a quantitative version of Enss' method to establish global-in-time decay estimates for solutions to Schr\"odinger equations on manifolds. To simplify the exposition we shall only consider Hamiltonians of the form $H…
In this paper, we study Hardy-type uncertainty principles and unique continuation properties for linear covariant Schrodinger equations with variable coefficients in the presence of bounded electric and magnetic potentials. Under suitable…
We prove a sharp version of the Hardy uncertainty principle for Schr\"odinger equations with external bounded electromagnetic potentials, based on logarithmic convexity properties of Schr\"odinger evolutions. We provide, in addition, an…
We consider the Chern-Simons-Schr\"odinger model in 1+2 dimensions, and prove scattering for small solutions of the Cauchy problem in the Coulomb gauge. This model is a gauge covariant Schr\"odinger equation, with a potential decaying like…
We show decay of the local energy of solutions of the charged Klein-Gordon equation in the exterior De Sitter-Reissner-Nordstr\"om spacetime by means of a resonance expansion of the local propagator.
We provide a uniform decay estimate of Morawetz type for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzchild background. This estimate is both uniform in space and time, so in particular it implies a…
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbation of unity with mild radial regularity. The key ingredient…
The optimality of decay properties of the one-dimensional damped wave equations with potentials belonging to a certain class is discussed. The typical ingredient is a variant of Nash inequality which involves an invariant measure for the…
In this paper we study the asymptotic phase space energy distribution of solution of the Schr\"{o}dinger equation with a time-dependent random potential. The random potential is assumed to be with slowly decaying correlations. We show that…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We prove sharp $L^\infty$ decay and modified scattering for a one-dimensional dispersion-managed cubic nonlinear Schr\"odinger equation with small initial data chosen from a weighted Sobolev space. Specifically, we work with an averaged…