The works presented in this volume originated in lectures on analysis in partial differential equations, given in at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences.

Included are: Jean-Yves Chemin, on profile decomposition and its applications to the Navier–Stokes system; Hongjie Dong, on Lp estimates for parabolic equations; Xiaochun Li, on the Hardy–Littlewood circle method; Fanghua Lin, on elliptic free boundary problems; Alexis Vasseur, on the De Giorgi method for elliptic and parabolic equations; Jiahong Wu, on 2D Boussinesq equations with partial or fractional dissipation; and Xiaoyi Zhang, on analytic tools for critical dispersive PDEs.