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

Estabelecimento in vitro de ápices caulinares de Liquidambar styraciflua.

Resumo

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

Validação de marcadores moleculares ligados a genes de resistência da ferrugem marrom para a ferrugem laranja da cana-de-açúcar.

RESUMO: Atualmente, a ferrugem alaranjada é a mais nova doença na cultura de cana-de-açúcar, causada pelo basidiomiceto Puccinia kuehnii. Nas regiões onde ocorre esse tipo de ferrugem, o controle é feito basicamente com o plantio de cultivares resistentes, porque o uso de fungicidas não é considerado prático e nem econômico. Além da ferrugem alaranjada, a ferrugem marrom causada pela Puccinia melanocephala é também encontrada no Brasil. A literatura já relatou vários marcadores relacionado ao gene principal de resistência a ferrugem marrom denominado Bru1 e o relato da ação de resistência deste gene a diversos isolados de fungo. Tendo-se em vista que a etiologia e sintomas da ferrugem marrom e ferrugem alaranjada são semelhantes, o objetivo deste trabalho foi validar alguns marcadores ligados ao gene de resistência a ferrugem marrom Bru1, para resistência a ferrugem alaranjada, através de triagem de variedades resistentes e susceptíveis por análises de PCR. Os resultados de análises de PCR, em 30 variedades de cana-de-açúcar, com dezoito pares de iniciadores relacionados ao gene de resistência à ferrugem marrom e 70 interações entre iniciadores localizados quase no mesmo sítio genômico, mostraram que apesar de algumas variações observadas entre variedades susceptíveis e resistentes, em algumas interações, o resultado não foi consistente para todas as variedades consideradas resistentes ou suscetíveis

Uniform regularity for the Navier-Stokes equation with Navier boundary condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in $L^\infty$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument

A posteriori error estimates for the virtual element method

An a posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing

The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.Comment: To appear in "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final publication is available at http://www.springerlink.co