Generalized Strichartz estimates for wave and Dirac equations in Aharonov–Bohm magnetic fields

Weighted Strichartz Estimates and Global Existence for Semilinear Wave Equations

where = ∂/∂t−∆x denotes the D’Alembertian. Our chief goal then is to find, for a given n, the sharp range of powers for which one always has a global weak solution of (1.2) if ε > 0 is small enough. Note that, even in the linear case, where one solves an inhomogeneous equation with a Lipschitz forcing term, in general one can only obtain weak solutions. An interesting problem would be to find o...

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 ...

Strichartz Estimates for Wave Equations with Coefficients of Sobolev Regularity

Wave packet techniques provide an effective method for proving Strichartz estimates on solutions to wave equations whose coefficients are not smooth. We use such methods to show that the existing results for C1,1 and C1,α coefficients can be improved when the coefficients of the wave operator lie in a Sobolev space of sufficiently high order.

Characteristic Strichartz Estimates for the Wave Equation

Strichartz 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...