Large time behavior for vortex evolution in the half-plane

In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic states for half-plane vortex dynamics decompose naturally into a nonlinear superposition of soliton-like states. Our approach is to combine techniques developed in the study of vortex confinement with weak convergence tools in order to study the asymptotic behavior of a self-similar rescaling of a solution of the incompressible 2D Euler equations on a half plane with compactly supported, nonnegative initial vorticity.Comment: 30 pages, no figure

FAKTOR-FAKTOR YANG MEMPENGARUHI EFEKTIVITAS GABUNGAN KELOMPOK TANI (GAPOKTAN) DALAM PROGRAM PENGEMBANGAN USAHA AGRIBISNIS PERDESAAN (PUAP) DI KECAMATAN PEDAN KABUPATEN KLATEN

n this paper we give the full classification of curves $C$ of genus $g$ such that a Brill--Noether locus $W^ s_d(C)$, strictly contained in the jacobian $J(C)$ of $C$, contains a variety $Z$ stable under translations by the elements of a positive dimensional abelian subvariety $A\subsetneq J(C)$ and such that $\dim(Z)=d-\dim(A)-2s$, i.e., the maximum possible dimension for such a $Z$

The limit of vanishing viscosity for the incompressible 3D Navier-Stokes equations with helical symmetry

In this paper, we are concerned with the vanishing viscosity problem for the three-dimensional Navier-Stokes equations with helical symmetry, in the whole space. We choose viscosity-dependent initial \bu_0^\nu with helical swirl, an analogue of the swirl component of axisymmetric flow, of magnitude $\mathcal{O}(\nu)$ in the $L^2$ norm; we assume \bu_0^\nu \to \bu_0 in $H^1$. The new ingredient in our analysis is a decomposition of helical vector fields, through which we obtain the required estimates.Comment: 22page

Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions

The second-grade fluid equations are a model for viscoelastic fluids, with two parameters: $\alpha > 0$, corresponding to the elastic response, and $\nu > 0$, corresponding to viscosity. Formally setting these parameters to $0$ reduces the equations to the incompressible Euler equations of ideal fluid flow. In this article we study the limits $\alpha, \nu \to 0$ of solutions of the second-grade fluid system, in a smooth, bounded, two-dimensional domain with no-slip boundary conditions. This class of problems interpolates between the Euler-$\alpha$ model ($\nu = 0$), for which the authors recently proved convergence to the solution of the incompressible Euler equations, and the Navier-Stokes case ($\alpha = 0$), for which the vanishing viscosity limit is an important open problem. We prove three results. First, we establish convergence of the solutions of the second-grade model to those of the Euler equations provided $\nu = \mathcal{O}(\alpha^2)$, as $\alpha \to 0$, extending the main result in [19]. Second, we prove equivalence between convergence (of the second-grade fluid equations to the Euler equations) and vanishing of the energy dissipation in a suitably thin region near the boundary, in the asymptotic regime $\nu = \mathcal{O}(\alpha^{6/5})$, $\nu/\alpha^2 \to \infty$ as $\alpha \to 0$. This amounts to a convergence criterion similar to the well-known Kato criterion for the vanishing viscosity limit of the Navier-Stokes equations to the Euler equations. Finally, we obtain an extension of Kato's classical criterion to the second-grade fluid model, valid if $\alpha = \mathcal{O}(\nu^{3/2})$, as $\nu \to 0$. The proof of all these results relies on energy estimates and boundary correctors, following the original idea by Kato.Comment: 20pages,1figur

Atopic Dermatitis Host and Environment Model: Revisiting Therapeutic Options

Atopic Dermatitis affects both children and adults and is a serious health concern in many countries. AD is a complex disease with host and environmental factors underlying its pathology. Its treatment is multidimensional reflecting the diverse nature of its triggers and includes emollients, topical steroids and calcineurin inhibitors among others. Immunological dysfunction can be addressed broadly with systemic immunosupressors and specifically with monoclonal antibodies. Dupilumab, which targets IL-4 and IL-13 was granted approval for treatment of moderate-to-severe AD. Biologics targeting IgE/Th2 pathways may have its role in patients with overlapping AD and asthma. Psychological distress can exacerbate symptoms and is associated with increased severity of AD. Environmental triggers, such as, allergens can be addressed in selected cases with allergic immunotherapy. In this paper, we discuss AD treatment and propose a new step-by-step approach aiming at maintaining disease control and improving quality of life.info:eu-repo/semantics/publishedVersio