446 research outputs found
Vanishing Viscosity Limits and Boundary Layers for Circularly Symmetric 2D Flows
We continue the work of Lopes Filho, Mazzucato and Nussenzveig Lopes [LMN],
on the vanishing viscosity limit of circularly symmetric viscous flow in a disk
with rotating boundary, shown there to converge to the inviscid limit in
-norm as long as the prescribed angular velocity of the
boundary has bounded total variation. Here we establish convergence in stronger
and -Sobolev spaces, allow for more singular angular velocities
, and address the issue of analyzing the behavior of the boundary
layer. This includes an analysis of concentration of vorticity in the vanishing
viscosity limit. We also consider such flows on an annulus, whose two boundary
components rotate independently.
[LMN] Lopes Filho, M. C., Mazzucato, A. L. and Nussenzveig Lopes, H. J.,
Vanishing viscosity limit for incompressible flow inside a rotating circle,
preprint 2006
Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains
We establish the resolvent estimates for the Stokes operator in
Lipschitz domains in , for . The result, in particular, implies that the Stokes operator in a
three-dimensional Lipschitz domain generates a bounded analytic semigroup in
for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a
conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the
Stokes operator in Lipschitz domain
Crack Bridging Mechanism for Glass Strengthening by Organosilane Water-Based Coatings
We used an epoxysilane/aminosilane coating deposited from an aqueous solution
to strengthen flat glass. We studied film formation, interfacial and mechanical
properties of the film. The film is highly cross-linked with a 6 GPa Young's
modulus and good adhesion. Our results suggest that crack face bridging
accounts for most of the 75 % reinforcement in this system
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Predicting and Controlling Resolution and Surface Finish of Ceramic Objects Produced by Stereodeposition Processes
Stereodeposition techniques are well suited for the Solid Freeform Fabrication of dense ceramic
components. As opposed to forming a pattern in a particle bed or polymer bath, stereodeposition
processes deposit material directly onto the previously created layer. The key to stereodeposition is
a material's ability to be dispensed as a fluid, yet rapidly stiffen to hold the shape of the object.
This is accomplished by either solidification of a thermoplastic binder upon cooling from a melt
(Fused Deposition) or by polymerization of a binder (Reactive Stereodeposition). We are
developing both techniques for the production of functional ceramic and engineering polymer
objects.
A key issue in developing a successful stereodeposition system is controlling the rate of bead
transformation from liquid to solid. Control is critical to achieving high resolution and low surface
roughness of the finished product, but is made complex by the large number of parameters
involved. These include binder parameters (surface tension, gelling characteristics), slurry
parameters (viscosity, particle loading and size distribution), and process parameters (deposition
rate, temperature). Current efforts at the University of Arizona are focused on modeling and
controlling the deposition and transformation of ceramic slurries used in the Reactive
Stereodeposition process.Mechanical Engineerin
Regularity estimates for the solution and the free boundary to the obstacle problem for the fractional Laplacian
We use a characterization of the fractional Laplacian as a Dirichlet to
Neumann operator for an appropriate differential equation to study its obstacle
problem. We write an equivalent characterization as a thin obstacle problem. In
this way we are able to apply local type arguments to obtain sharp regularity
estimates for the solution and study the regularity of the free boundary
Sharp constants in weighted trace inequalities on Riemannian manifolds
We establish some sharp weighted trace inequalities
W^{1,2}(\rho^{1-2\sigma}, M)\hookrightarrow L^{\frac{2n}{n-2\sigma}}(\pa M)
on dimensional compact smooth manifolds with smooth boundaries, where
is a defining function of and . This is stimulated
by some recent work on fractional (conformal) Laplacians and related problems
in conformal geometry, and also motivated by a conjecture of Aubin.Comment: 34 page
Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces
In this paper we present a survey of the joint program with Fabrice Baudoin
originated with the paper \cite{BG1}, and continued with the works \cite{BG2},
\cite{BBG}, \cite{BG3} and \cite{BBGM}, joint with Baudoin, Michel Bonnefont
and Isidro Munive.Comment: arXiv admin note: substantial text overlap with arXiv:1101.359
Parabolic oblique derivative problem in generalized Morrey spaces
We study the regularity of the solutions of the oblique derivative problem
for linear uniformly parabolic equations with VMO coefficients. We show that if
the right-hand side of the parabolic equation belongs to certain generalized
Morrey space than the strong solution belongs to the corresponding generalized
Sobolev-Morrey space
The mixed problem for the Laplacian in Lipschitz domains
We consider the mixed boundary value problem or Zaremba's problem for the
Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on
part of the boundary and Neumann data on the remainder of the boundary. We
assume that the boundary between the sets where we specify Dirichlet and
Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p
and the Dirichlet data is in the Sobolev space of functions having one
derivative in L^p for some p near 1. Under these conditions, there is a unique
solution to the mixed problem with the non-tangential maximal function of the
gradient of the solution in L^p of the boundary. We also obtain results with
data from Hardy spaces when p=1.Comment: Version 5 includes a correction to one step of the main proof. Since
the paper appeared long ago, this submission includes the complete paper,
followed by a short section that gives the correction to one step in the
proo
Green's functions for parabolic systems of second order in time-varying domains
We construct Green's functions for divergence form, second order parabolic
systems in non-smooth time-varying domains whose boundaries are locally
represented as graph of functions that are Lipschitz continuous in the spatial
variables and 1/2-H\"older continuous in the time variable, under the
assumption that weak solutions of the system satisfy an interior H\"older
continuity estimate. We also derive global pointwise estimates for Green's
function in such time-varying domains under the assumption that weak solutions
of the system vanishing on a portion of the boundary satisfy a certain local
boundedness estimate and a local H\"older continuity estimate. In particular,
our results apply to complex perturbations of a single real equation.Comment: 25 pages, 0 figur
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