Gaussian Decay of the Magnetic Eigenfunctions.
General highly accurate algebraic coarsening.
Global existence of large amplitude solutions for nonlinear massless Dirac equation
Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field.
Global maximal estimates for solutions to the Schrödinger equation
Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.
Global well-posedness and scattering for the defocusing -subcritical Hartree equation in
Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling
Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in under some conditions on the nonlinearity (the coupling term), by using the conservation law for and controlling the growth of via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007)...
Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case
We establish global existence and scattering for radial solutions to the energy-critical focusing Hartree equation with energy and Ḣ¹ norm less than those of the ground state in , d ≥ 5.
Growth and accretion of mass in an astrophysical model
We study asymptotic behavior of radial solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles. In particular, we consider stationary solutions in balls and in the whole space, self-similar solutions defined globally in time, blowing up self-similar solutions, and singularities of solutions that blow up in a finite time.