44 citations · 265 across the 51 of their papers we have counts for
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Ground state energy threshold and blow-up for NLS with competing nonlinearities
Jacopo Bellazzini, Luigi Forcella, Vladimir Georgiev
We consider the nonlinear Schrödinger equation with combined nonlinearities, where the leading term is an intracritical focusing power-type nonlinearity, and the perturbation is gi…
Necessary and sufficient condition for global existence of solutions for 1D periodic NLS with non-gauge invariant quadratic nonlinearity
Kazumasa Fujiwara, Vladimir Georgiev
We study 1D NLS with non-gauge invariant quadratic nonlinearity on the torus. The Cauchy problem admits trivial global solutions which are constant with respect to space. The non-e…
Blowup dynamics for Mass Critical Half-wave equation in 3D
Vladimir Georgiev, Yuan Li
We consider the half-wave equation in three dimension and in the mass critical. For initial data with…
Nondispersive solutions to the mass critical half-wave equation in two dimensions
Vladimir Georgiev, Yuan Li
We consider the half-wave equation with mass critical in two dimension \begin{eqnarray*} \begin{cases} iu_t=Du-|u|u,\,\,\, \\ u(0,x)=u_0(x), \end{cases} \end{eqnarray*} First, we p…
Global Large Data Solutions of 2D Dirac Equation with Hartree Type Interaction
Vladimir Georgiev, Boris Shakarov
Local and global well - posedness of the solution to the two space dimensional Dirac equation with Hartree type nonlinearity is established with the initial datum in the space $H^s…