Vortex sheets with reflection symmetry in exterior domains

AbstractIn this paper we prove the existence of a weak solution of the incompressible 2D Euler equations in the exterior of a reflection symmetric smooth bluff body with symmetric initial flow corresponding to vortex sheet type data whose vorticity is of distinguished sign on each side of the symmetry axis. This work extends the results proved for full plane flow by the authors in [M.C. Lopes Filho, H.J. Nussenzveig Lopes, Z. Xin, Existence of vortex sheets with reflection symmetry in two space dimensions, Arch. Ration. Mech. Anal. 158 (3) (2001) 235–257]

An Extension Of Marchioro's Bound On The Growth Of A Vortex Patch To Flows With Lp Vorticity

We observe that C. Marchioro's cubic-root bound in time on the growth of the diameter of a patch of vorticity [Comm. Math. Phys, 164 (1994), pp. 507-524] can be extended to incompressible two-dimensional Euler flows with compactly supported initial vorticity in Lp, p > 2, and with a distinguished sign.293596599Delort, J.-M., Existence de nappes de tourbillons en dimension deux (1991) J. Amer. Math. Soc., 4, pp. 553-586Majda, A., Vorticity and the mathematical theory of incompressible fluid flow (1986) Comm. Pure Appl. Math., 39, pp. S187-S220Marchioro, C., Bounds on the growth of the support of a vortex patch (1994) Comm. Math. Phys., 164, pp. 507-524Schocket, S., The weak vorticity formulation of the 2D Euler equations and concentration-cancellation (1995) Comm. Partial Differential Equations, 20, pp. 1077-110

Nonlinear stabilitty for steady vortex pairs

In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin's variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.Comment: 25 page

The Vortex-Wave equation with a single vortex as the limit of the Euler equation

In this article we consider the physical justification of the Vortex-Wave equation introduced by Marchioro and Pulvirenti in the case of a single point vortex moving in an ambient vorticity. We consider a sequence of solutions for the Euler equation in the plane corresponding to initial data consisting of an ambient vorticity in $L^1\cap L^\infty$ and a sequence of concentrated blobs which approach the Dirac distribution. We introduce a notion of a weak solution of the Vortex-Wave equation in terms of velocity (or primitive variables) and then show, for a subsequence of the blobs, the solutions of the Euler equation converge in velocity to a weak solution of the Vortex-Wave equation.Comment: 24 pages, to appea

Detection of periodontal pathogens in mothers of preterm birth and/or low weight

The present study aims to estimate the possible relationship between periodontal pathogens in the oral cavity and the birth of Preterm Birth (PTB) and/or Low Birth Weight (LBW). It?s a case- control study with the subgengival biofilm samples were collected from four sites up deeper until 48 hours postpartum and were processes by Polymerase Chain Reaction (PCR) for presence the periodontal pathogens Prevotella intermedia (Pi), Fusobacterium nucleatum (Fn), Porphyromonas gingivalis (Pg), Treponema denticola (Td),  Tannerella forsythia (Tf) e Aggregatibacter actinomycetemcomitans (Aa). The mothers were divided into case grup (babies weighing < 2500g and/or gestational age < 37 weeks) and control group (babies weighing ? 2500g and gestational age ? 37 weeks). Chi-square test and the measure of association obtained by Odds Ratio (OR) were used to estimate the association between the variables. Microbial analyses results showed no significant association between PTB and LBW with most periodontal pathogens in the oral cavity, even with association with the clinical presence of periodontitis. given the high presence of periodontal pathogens in the biofilm subgengival of recent mothers, it is suggested that the findings of this research serve as the basis for future studies on the pathophysiology involved in the relationship between periodontitis and PTB and/or LBW

Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and L^\infty((0,T)\times\o), where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.Comment: 45page