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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...

V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa: On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann...

These proceedings contain original research articles by specialists from many countries on a wide variety of aspects of Navier-Stokes equations. Additionally, two survey articles intended for a wider readership discuss the present state of the subject via open problems, and deal with the interplay between theory and numerical analysis.