This volume contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirao da Veiga's 70th birthday, held from February 17-21, 2014, in Levico Terme, Italy. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide-ranging influence of Hugo Beirao da Veiga on the field of partial differential equations, in particular those related to fluid dynamics. In his own...