Smoothing - Strichartz Estimates for the Schrödinger Equation with Small Magnetic Potential Vladimir Georgiev, Atanas Stefanov and Mirko Tarulli
نویسنده
چکیده
The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is discussed too. 2000 Mathematics Subject Classification: 35Q40; 35F25.
منابع مشابه
Smoothing - Strichartz Estimates for the Schrödinger Equation with Small Magnetic Potential
The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is disc...
متن کاملScale invariant energy smoothing estimates for the Schrödinger equation with small magnetic potential
We consider some scale invariant generalizations of the smoothing estimates for the free Schrödnger equation obtained by Kenig, Ponce and Vega in [21], [22]. Applying these estimates and using appropriate commutator estimates, we obtain similar scale invariant smoothing estimates for perturbed Schrödnger equation with small magnetic potential.
متن کاملStrichartz 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 کاملGlobal Regularity for the Quadratic Klein-gordon Equation in R1+2
We consider 2-D Klein Gordon equation with quadratic nonlinearity and prove Strichartz type dispersive estimates for the global solution with small initial data in the Sobolev space H.
متن کاملOn Quadratic Derivative Schrödinger Equations in One Space Dimension
We consider the Schrödinger equation with derivative perturbation terms in one space dimension. For the linear equation, we show that the standard Strichartz estimates hold under specific smallness requirements on the potential. As an application, we establish existence of local solutions for quadratic derivative Schrödinger equations in one space dimension with small and rough Cauchy data.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005