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 work, da Veiga has been a seminal influence in many important areas: Navier-Stokes equations, Stokes systems, non-Newtonian fluids, Euler equations, regularity of solutions, perturbation theory, vorticity phenomena, and nonlinear potential theory, as well as various degenerate or singular models in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.

Table of Contents:
A. Sequeira, J.-P. Dias, A. Valli, P. Secchi, L. Berselli, and F. Crispo, Tributes to Hugo Beirao da Veiga H. A. Baba, C. Amrouche, and M. Escobedo, Analyticity of the semi-group generated by the Stokes operator with Navier-type boundary conditions on $L^p$-spaces P. Antonelli and P. Marcati, Some results on systems for quantum fluids C. Bardos and T. T. Nguyen, Remarks on the inviscid limit for the compressible flows V. Benci and L. L. Baglini, A generalization of Gauss' divergence theorem L. C. Berselli and S. Spirito, Weak solutions to the Navier-Stokes equations constructed by semi-discretization are suitable D. Breit, Existence theory for generalized Newtonian fluids G. Buttazzo and B. Velichkov, The spectral drop problem D. Chae, On the vanishing theorems for the discretely self-similar solutions to the Hall equations F. Crispo and P. Maremonti, A high regularity result of solutions to a modified $p$-Navier-Stokes system R. Farwig, C. Simader, H. Sohr, and W. Varnhorn, General properties of the Helmholtz decomposition in spaces of $L^q$-type E. Feireisl and Y. Sun, Conditional regularity of very weak solutions to the Navier-Stokes-Fourier system F. Flandoli, Possible effect of noise on stretching mechanism G. P. Galdi and C. R. Grisanti, On the plane steady-state flow of a shear-thinning liquid past an obstacle in the singular case V. Georgiev and A. R. Giammetta, Sectorial Hamiltonians without zero resonance in one dimension Z. Grujic, Vortex stretching and anisotropic diffusion in the 3D Navier-Stokes equations P. Kaplicky, On $L^q$ estimates for planar flows up to boundary B. Ducomet and S. Necasova, Non equilibrium diffusion limit in a barotropic radiative flow R. Rautmann, Decomposition of the homogeneous space $\hat{W}^{1,2}$ with respect to the Dirichlet form $\langle \nabla u,\nabla v \rangle$ and applications S. Rionero, Convection in ternary porous layers with depth-dependent permeability and viscosity F. Miranda and J. F. Rodrigues, On a variational inequality for incompressible non-Newtonian thick flows E. Molitor and M. Ruzicka, On inhomogeneous $p$-Navier-Stokes systems Y. Shibata, On the global well-posedness of some free boundary problem for a compressible barotropic viscous fluid flow V. A. Solonnikov, On a free boundary problem of magnetohydrodynamics for a viscous incompressible fluid not subjected to capillary forces A. F. Vasseur, Relative entropy and contraction for extremal shocks of conservation laws up to a shift.