This Research Note presents some recent advances in various important domains of partial differential equations and applied mathematics, in particular for calculus of variations and fluid flows. These topics are now part of various areas of science and have experienced tremendous development during the last decades.

Preface
CALCULUS OF VARIATIONS
Partial regularity in free discontinuity problems
A duality proof of the Hille-Yosida theorem
Ginzburg-Landau equations and Pohozaev identity
Closure theorems in BV setting
Shape continuity for Dirichlet-Neumann problems
Multiple solutions for a class of eigenvalue problems in hemivariational inequalities
Equivariant harmonic maps and pendulum-type equations
Isoperimetric inequalities and calibrations
On some non convex variational problems
Binding of Schroedinger particles through conspiracy of potential wells in 4
The p-Laplace system involving measure data
Nonlinear diffusion with absorption
FLUID FLOWS
Space-time integrated least-squares: a simple, stable and precise finite element scheme to solve advection equations as if they were elliptic
On the uniqueness of the solution of the dam problem with leaky boundary conditions
The Stokes system in 3D-Lipschitz domains: a survey of recent results
Partial regularity and weighted energy estimates of global weak so lutions of the Navier-Stokes system
Breaking the dimension of solitary waves
Heat propagation in an inhomogeneous medium

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