Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and applications

A Physical Space Proof of the Bilinear Strichartz and Local Smoothing Estimates for the Schrödinger Equation

Let d ≥ 1, and let u, v : R × R → C be Schwartz space solutions to the Schrödinger equation iut + ∆xu = 0; ivt + ∆xv = 0. The standard L bilinear Strichartz estimate for the Schrödinger equation asserts that ‖uv‖L2t,x(R×Rd) .d M N‖u(0)‖L2x(Rd)‖v(0)‖L2x(Rd) whenever u, v are supported in frequency regions {ξ ∈ R : N ≤ |ξ| ≤ 2N}, {η ∈ R : M ≤ |η| ≤ 2M}, and N ≥ 4M . This estimate has been used ex...

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.

Strichartz Estimates for the Schrödinger Equation

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.

Characteristic Strichartz Estimates for the Wave Equation

Strichartz 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...