Hichem Hajaiej

Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity

This paper is devoted to the mathematical analysis of a class of nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We show the well-posedness of the associated Cauchy problem and prove the existence and stability of standing waves under suitable assumptions on the nonlinearity. Our proofs rely on a contraction argument in mixed functional spaces and the concentration-compactness method.

MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE

In [Setting and analysis of the multi-configuration time-dependent Hartree–Fock equations, Arch. Ration. Mech. Anal.198 (2010) 273–330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree–Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number Ncr.

On the spin-1 Bose–Einstein condensates in the presence of Ioffe–Pritchard magnetic field

We study the Cauchy problem of an antiferromagnetic spin-1 Bose–Einstein condensate under Ioffe–Pritchard magnetic field B. We then address the existence of ground state solutions and characterize the orbit of standing waves.

Characterization of Maximizers via Mass Transportation Techniques

In this paper, we address the question of existence and uniqueness of maximizers of a class of functionals under constraints, via mass transportation theory. We also determine suitable assumptions ensuring that balls are the unique maximizers. In both cases, we show that our hypotheses are optimal.

Existence and uniqueness of maximizers of a class of functionals under constraints: optimal conditions

In this article, we establish optimal assumptions under which general Hardy-Littlewood and Riesz-type functionals are maximized by balls. We also determine additional hypotheses such that balls are the unique maximizers. In both cases, we prove that our assumptions are optimal.