A Kato type Theorem for the inviscid limit of the Navier-Stokes equations with a moving rigid body

The issue of the inviscid limit for the incompressible Navier-Stokes equations when a no-slip condition is prescribed on the boundary is a famous open problem. A result by Tosio Kato says that convergence to the Euler equations holds true in the energy space if and only if the energy dissipation rate of the viscous flow in a boundary layer of width proportional to the viscosity vanishes. Of course, if one considers the motion of a solid body in an incompressible fluid, with a no-slip condition at the interface, the issue of the inviscid limit is as least as difficult. However it is not clear if the additional difficulties linked to the body's dynamic make this issue more difficult or not. In this paper we consider the motion of a rigid body in an incompressible fluid occupying the complementary set in the space and we prove that a Kato type condition implies the convergence of the fluid velocity and of the body velocity as well, what seems to indicate that an answer in the case of a fixed boundary could also bring an answer to the case where there is a moving body in the fluid

Existence of global strong solutions to a beam-fluid interaction system

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure

Failure to up-regulate VEGF165b in maternal plasma is a first trimester predictive marker for pre-eclampsia

Pre-eclampsia is a pregnancy-related condition characterized by hypertension, proteinuria and endothelial dysfunction. VEGF165b, formed by alternative splicing of VEGF (vascular endothelial growth factor) pre-mRNA, inhibits VEGF165-mediated vasodilation and angiogenesis, but has not been quantified in pregnancy. ELISAs were used to measure means±S.E.M. plasma VEGF165b, sEng (soluble endoglin) and sFlt-1 (soluble fms-like tyrosine kinase-1). At 12 weeks of gestation, the plasma VEGF165b concentration was significantly up-regulated in plasma from women who maintained normal blood pressure throughout their pregnancy (normotensive group, 4.90±1.6 ng/ml; P<0.01, as determined using a Mann-Whitney U test) compared with non-pregnant women (0.40±0.22 ng/ml). In contrast, in patients who later developed pre-eclampsia, VEGF165b levels were lower than in the normotensive group (0.467±0.209 ng/ml), but were no greater than non-pregnant women. At term, plasma VEGF165b concentrations were greater than normal in both pre-eclamptic (3.75±2.24 ng/ml) and normotensive (10.58 ng/ml±3.74 ng/ml; P>0.1 compared with pre-eclampsia) pregnancies. Patients with a lower than median plasma VEGF165b at 12 weeks had elevated sFlt-1 and sEng pre-delivery. Concentrations of sFlt-1 (1.20±0.07 and 1.27±0.18 ng/ml) and sEng (4.4±0.18 and 4.1±0.5 ng/ml) were similar at 12 weeks of gestation in the normotensive and pre-eclamptic groups respectively. Plasma VEGF165b levels were elevated in pregnancy, but this increase is delayed in women that subsequently develop pre-eclampsia. In conclusion, low VEGF165b may therefore be a clinically useful first trimester plasma marker for increased risk of pre-eclampsia

Multi-scale analysis of compressible viscous and rotating fluids

We study a singular limit for the compressible Navier-Stokes system when the Mach and Rossby numbers are proportional to certain powers of a small parameter \ep. If the Rossby number dominates the Mach number, the limit problem is represented by the 2-D incompressible Navier-Stokes system describing the horizontal motion of vertical averages of the velocity field. If they are of the same order then the limit problem turns out to be a linear, 2-D equation with a unique radially symmetric solution. The effect of the centrifugal force is taken into account

On the ill/well-posedness and nonlinear instability of the magneto-geostrophic equations

We consider an active scalar equation that is motivated by a model for magneto-geostrophic dynamics and the geodynamo. We prove that the non-diffusive equation is ill-posed in the sense of Hadamard in Sobolev spaces. In contrast, the critically diffusive equation is well-posed. In this case we give an example of a steady state that is nonlinearly unstable, and hence produces a dynamo effect in the sense of an exponentially growing magnetic field.Comment: We have modified the definition of Lipschitz well-posedness, in order to allow for a possible loss in regularity of the solution ma

Direct mass measurements of 19B, 22C, 29F, 31Ne, 34Na and other light exotic nuclei

We report on direct time-of-flight based mass measurements of 16 light neutron-rich nuclei. These include the first determination of the masses of the Borromean drip-line nuclei $^{19}$B, $^{22}$C and $^{29}$F as well as that of $^{34}$Na. In addition, the most precise determinations to date for $^{23}$N and $^{31}$Ne are reported. Coupled with recent interaction cross-section measurements, the present results support the occurrence of a two-neutron halo in $^{22}$C, with a dominant $\nu2s_{1/2}^2$ configuration, and a single-neutron halo in $^{31}$Ne with the valence neutron occupying predominantly the 2$p_{3/2}$ orbital. Despite a very low two-neutron separation energy the development of a halo in $^{19}$B is hindered by the 1$d_{5/2}^2$ character of the valence neutrons.Comment: 5 page

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective