This paper is concerned with the positive ground state solutions for a quasilinear Schrodinger equation with a Hardy-type term.We obtain positive ground state solutions for the given quasilinear Schrodinger equation by using a change of variables and variational method.
We propose a hybrid quantum-classical method,the quantum-enriched large eddy simulation(QELES),for simulating turbulence.The QELES combines the large-scale motion of the large eddy simulation(LES)and the subgrid motion of the incompressible Schrodinger flow(ISF).The ISF is a possible way to be simulated on a quantum computer,and it generates subgrid scale turbu-lent structures to enrich the LES field.The enriched LES field can be further used in turbulent combustion and multi-phase flows in which the subgrid scale motion plays an important role.As a conceptual study,we perform the simulations of ISF and LES separately on a classical computer to simulate decaying homogeneous isotropic turbulence.Then,the QEI ES velocity is obtained by the time matching and the spectral blending methods.The QEL ES achieves significant improvement in predicting the energy spectrum,probaility density functions of velocity and vorticity components,and velocity structure functions,and reconstructs coherent small-scales vortices in the direct numerical simulation(DNS).On the other hand,the vortices in the QELES are less elongated and tangled than those in the DNS,and the magnitude of the third-order structure function in the QELES is less than that in the DNS,due to the diferent constitutive relations in the viscous flow and ISE.
