Relaxation Limit from the Quantum Navier–Stokes Equations to the Quantum Drift–Diffusion Equation

The relaxation-time limit from the Quantum-Navier-Stokes-Poisson system to quantum drift-diffusion equation is performed in framework of finite energy weak solutions. No assumptions on limiting solution are made. proof exploits suitably scaled a priori bounds inferred by and BD entropy estimates. Moreover, it shown how those estimates Fisher free associated diffusive evolution recovered limit. As byproduct, our main result also provides an alternative for existence solutions equation.