Strichartz Estimates for the Schrödinger Equation

نویسندگان

  • ELENA CORDERO
  • DAVIDE ZUCCO
  • Elena Cordero
  • Davide Zucco
چکیده

The objective of this paper is to report on recent progress on Strichartz estimates for the Schrödinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in Wiener amalgam and modulation spaces. We present and compare the different technicalities. Then, we illustrate applications to well-posedness.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Strichartz Estimates for the Magnetic Schrödinger Equation

We prove global, scale invariant Strichartz estimates for the linear magnetic Schrödinger equation with small time dependent magnetic field. This is done by constructing an appropriate parametrix. As an application, we show a global regularity type result for Schrödinger maps in dimensions n ≥ 6.

متن کامل

Some New Strichartz Estimates for the Schrödinger Equation

We deal with fixed-time and Strichartz estimates for the Schrödinger propagator as an operator on Wiener amalgam spaces. We discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones. As an application, we present a result on the wellposedness of the linear Schrödinger equation with a rough time dependent potential.

متن کامل

Counterexamples to Strichartz Estimates for the Magnetic Schrödinger Equation

In space dimension n ≥ 3, we consider the magnetic Schrödinger Hamiltonian H = −(∇− iA(x)) and the corresponding Schrödinger equation i∂tu + Hu = 0. We show some explicit examples of potentials A, with less than Coulomb decay, for which any solution of this equation cannot satisfy Strichartz estimates, in the whole range of Schrödinger admissibility.

متن کامل

The Schrödinger equation on a compact manifold : Strichartz estimates and applications

We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation on any riemannian compact manifold. As a consequence we infer global existence results for the Cauchy problem of nonlinear Schrödinger equations on surfaces in the case of defocusing polynomial nonlinearities, and on three–manifolds in the case of quadratic nonlinearities. We also discuss the optimali...

متن کامل

Strichartz Estimates in Wiener Amalgam Spaces for the Schrödinger Equation

We study the dispersive properties of the Schrödinger equation. Precisely, we look for estimates which give a control of the local regularity and decay at infinity separately. The Banach spaces that allow such a treatment are the Wiener amalgam spaces, and Strichartz-type estimates are proved in this framework. These estimates improve some of the classical ones in the case of large time.

متن کامل

Spherically Averaged Endpoint Strichartz Estimates for the Two-dimensional Schrödinger Equation

X iv :m at h/ 98 11 16 8v 1 [ m at h. A P] 2 9 N ov 1 99 8 Abstract. The endpoint Strichartz estimates for the Schrödinger equation is known to be false in two dimensions[7]. However, if one averages the solution in L in the angular variable, we show that the homogeneous endpoint and the retarded half-endpoint estimates hold, but the full retarded endpoint fails. In particular, the original ver...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010