Reprinted from the Chinese annals of mathematics, the 18 papers in this collection report recent results in mathematical analysis, geometry, numerical methods, fluid mechanics, and control theory. The authors investigate the stability of a steady ideal plane flow, the regularity theory for systems of partial differential equations with Neumann boundary conditions, operator-splitting methods for the simulation of Bingham visco-plastic flow, and iterative algorithms for data assimilation problems. The opening chapters remember the life and achievements of Professor Lions.