Strichartz Estimates for Charge Transfer Models
نویسندگان
چکیده
In this note, we prove Strichartz estimates for scattering states of scalar charge transfer models in R3. Following the idea of Strichartz estimates based on [3, 10], we also show that the energy of the whole evolution is bounded independently of time without using the phase space method, as for example, in [5]. One can easily generalize our arguments to Rn for n ≥ 3. We also discuss the extension of these results to matrix charge transfer models in R3.
منابع مشابه
Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians
We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R3: ∂ttu− ∆u + m ∑ j=1 Vj (x− ~vjt)u = 0. The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates ...
متن کاملStrichartz Estimates for Some 2D Water Wave Models
In this paper we establish Strichartz type estimates associated with a class of semigroup operators in Rn, which for n = 2 correspond to some 2D water wave models. We also establish a nonlinear scattering result for solutions of the generalized Benney-Luke equation for higher order nonlinearity and small data initial in the energy space.
متن کاملStrichartz Type Estimates for Fractional Heat Equations
We obtain Strichartz estimates for the fractional heat equations by using both the abstract Strichartz estimates of Keel-Tao and the HardyLittlewood-Sobolev inequality. We also prove an endpoint homogeneous Strichartz estimate via replacing L∞x (R ) by BMOx(R) and a parabolic homogeneous Strichartz estimate. Meanwhile, we generalize the Strichartz estimates by replacing the Lebesgue spaces with...
متن کاملStrichartz Estimates for the Kinetic Transport Equation
We prove Strichartz estimates for the kinetic transport equation employing the techniques of Keel and Tao [11] and Foschi [8]. Our results extend considerably the range of the known Strichartz estimates in the literature for that equation. We show sharpness to most of the estimates that we prove. In particular, in one spatial dimension we find the full range of validity of the Strichartz estima...
متن کاملStrichartz Estimates for Long Range Perturbations
— We study local in time Strichartz estimates for the Schrödinger equation associated to long range perturbations of the flat Laplacian on the euclidean space. We prove that in such a geometric situation, outside of a large ball centered at the origin, the solutions of the Schrödinger equation enjoy the same Strichartz estimates as in the non perturbed situation. The proof is based on the Isoza...
متن کامل