LOW REGULARITY SOLUTIONS TO HIGHER-ORDER HARTREE-FOCK EQUATIONS WITH UNIFORM BOUNDS

LOW REGULARITY SOLUTIONS TO HIGHER-ORDER HARTREE-FOCK EQUATIONS WITH UNIFORM BOUNDS

In this paper, we consider the higher-order Hartree-Fock equations. The higher-order linear Schr¨odinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudo-relativistic linear Schr¨odinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L2 space but also proved that the solutions stay bounded uniformly in c