In this paper, we extend some results proved in previous references for three-dimensional Navier-Stokes equations. We show that when the norm of the velocity field is small enough in $L^3({I!!R}^3)$, then a global smooth solution of the Navier-Stokes
equations is ensured. We show that a similar result holds when the norm of the velocity field is small enough in $H^{frac{1}{2}}({I!!R}^3)$. The scale invariance of these two norms is discussed.
Photon-photon interactions represent an important class of physics processes at the LHC, where quasi-real photons are emitted by both colliding protons. These reactions can result in the exclusive production of a final state $X$, $p+p rightarrow p+p+
X$. When computing such cross sections, it has already been shown that finite size effects of colliding protons are important to consider for a realistic estimate of the cross sections. These first results have been essential in understanding the physics case of heavy-ion collisions in the low invariant mass range, where heavy ions collide to form an exclusive final state like a $J/Psi$ vector meson. In this paper, our purpose is to present some calculations that are valid also for the exclusive production of high masses final states in proton-proton collisions, like the production of a pair of $W$ bosons or the Higgs boson. Therefore, we propose a complete treatment of the finite size effects of incident protons irrespective of the mass range explored in the collision. Our expectations are shown to be in very good agreement with existing experimental data obtained at the LHC.
A new experimental analysis of the diffractive process $ep rightarrow eXY$, where $Y$ denotes a proton or its low mass excitation with $M_Y<1.6$ GeV, has been performed with the H1 experiment at HERA cite{Aaron:2012ad}. The main results of this study
are summarised in this document, together with the comparisons to other measurements and theoretical predictions.
Standard parton distribution functions contain neither information on the correlations between partons nor on their transverse motion, then a vital knowledge about the three dimensional structure of the nucleon is lost. Hard exclusive processes, in p
articular DVCS, are essential reactions to go beyond this standard picture. In the following, we examine the most recent data and their implication on the quarks/gluons imaging (tomography) of the nucleon.
