Almost sure existence of global weak solutions for super-critical Navier-Stokes equations

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for which global energy bounds are proved. As a consequence, we obtain almost sure super-critical global weak solutions. We also show that in 2d these global weak solutions are unique.Comment: 22 pages, a revised argument in Section 5, the $d=3$ cas

The Cauchy problem for metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field

We study the initial value formulation of metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field acting as source of the field equations. Sufficient conditions for the well-posedness of the Cauchy problem are formulated. This result completes the analysis of the same problem already considered for other sources.Comment: 6 page

Improved modelling of helium and tritium production for spallation targets

Reliable predictions of light charged particle production in spallation reactions are important to correctly assess gas production in spallation targets. In particular, the helium production yield is important for assessing damage in the window separating the accelerator vacuum from a spallation target, and tritium is a major contributor to the target radioactivity. Up to now, the models available in the MCNPX transport code, including the widely used default option Bertini-Dresner and the INCL4.2-ABLA combination of models, were not able to correctly predict light charged particle yields. The work done recently on both the intranuclear cascade model INCL4, in which cluster emission through a coalescence process has been introduced, and on the de-excitation model ABLA allows correcting these deficiencies. This paper shows that the coalescence emission plays an important role in the tritium and $^3He$ production and that the combination of the newly developed versions of the codes, INCL4.5-ABLA07, now lead to good predictions of both helium and tritium cross sections over a wide incident energy range. Comparisons with other available models are also presented.Comment: 6 pages, 9 figure

Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations

In this article, we consider a special class of initial data to the 3D Navier-Stokes equations on the torus, in which there is a certain degree of orthogonality in the components of the initial data. We showed that, under such conditions, the Navier-Stokes equations are globally wellposed. We also showed that there exists large initial data, in the sense of the critical norm $B^{-1}_{\infty,\infty}$ that satisfies the conditions that we considered.Comment: 13 pages, updated references for v

Motion of Isolated bodies

It is shown that sufficiently smooth initial data for the Einstein-dust or the Einstein-Maxwell-dust equations with non-negative density of compact support develop into solutions representing isolated bodies in the sense that the matter field has spatially compact support and is embedded in an exterior vacuum solution

A certain necessary condition of potential blow up for Navier-Stokes equations

We show that a necessary condition for $T$ to be a potential blow up time is $\lim\limits_{t\uparrow T}\|v(\cdot,t)\|_{L_3}=\infty$.Comment: 16 page

The "Symplectic Camel Principle" and Semiclassical Mechanics

Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002