Optimal convergence rate of nonrelativistic limit for the nonlinear pseudo-relativistic equations

Abstract

In this paper, we are concerned with the nonrelativistic limit of the following pseudo-relativistic equation with Hartree nonlinearity or power type nonlinearity \[ \left(\sqrt{-\hbar^2c^2 Δ+m^2c^4} - mc^2 \right) u + μu = \mathcal{N}(u), \] where $c$ denotes the speed of light. We prove that the ground states of this equation converges to the ground state of its nonrelativistic counterpart \[ -\frac{\hbar^2}{2m}Δu + μu = \mathcal{N}(u) \] with an explicit convergence rate $1/c^2$ in arbitrary order as $c\to \infty$. Moreover, we show that this rate is optimal.

23 pages, title and abstract were modified

References in corpus (1)

• Nonrelativistic limit of standing waves for pseudo-relativistic nonlinear Schrödinger equations

Cited by in corpus (2)

• On critical and supercritical pseudo-relativistic nonlinear Schrödinger equations
• Uniqueness and symmetry of ground states for higher-order equations