21 research outputs found
Singular limit of 2D second grade fluid past an obstacle
In this paper, we consider the 2D second grade fluid past an obstacle
satisfying the standard non-slip boundary condition at the surface of the
obstacle. Second grade fluid model is a well-known non-Newtonian model, with
two parameters: representing length-scale, while
corresponding to viscosity. We prove that, under the constraint condition , the second grade fluid with a suitable initial
velocity converges to the Euler fluid as tends to zero. Moreover, we
estimate the convergence rate of the solution of second grade fluid equations
to the one of Euler fluid equations as and approach zero
Global Well-Posedness of 2D Second Grade Fluid Equations in Exterior Domain
In this article, we consider 2D second grade fluid equations in exterior
domain with Dirichlet boundary conditions. For initial data , the system is shown to be global well-posed.
Furthermore, for arbitrary and , we prove that the solution
belongs to provided that
is in
Stability and inviscid limit of the 3D anisotropic MHD system near a background magnetic field with mixed fractional partial dissipation
A main result of this paper establishes the global stability of the
three-dimensional MHD equations near a background magnetic field with mixed
fractional partial dissipation with . Namely,
the velocity equations involve dissipation with the case and
. The magnetic equations without partial magnetic diffusion
but with the diffusion , where
with are the directional fractional
operators. Then we focus on the vanishing vertical kinematic viscosity
coefficient limit of the MHD system with the case to the case
. The convergent result is obtained in the sense of -norm
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: , corresponding to the elastic response, and , corresponding to viscosity. Formally setting these parameters to
reduces the equations to the incompressible Euler equations of ideal fluid
flow. In this article we study the limits 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- model (), for which the authors recently proved
convergence to the solution of the incompressible Euler equations, and the
Navier-Stokes case (), 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 , as , 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 ,
as . 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 , as . The proof of all these results
relies on energy estimates and boundary correctors, following the original idea
by Kato.Comment: 20pages,1figur
Convergence of the 2D Euler- to Euler equations in the Dirichlet case: indifference to boundary layers
In this article we consider the Euler- system as a regularization of
the incompressible Euler equations in a smooth, two-dimensional, bounded
domain. For the limiting Euler system we consider the usual non-penetration
boundary condition, while, for the Euler- regularization, we use
velocity vanishing at the boundary. We also assume that the initial velocities
for the Euler- system approximate, in a suitable sense, as the
regularization parameter , the initial velocity for the limiting
Euler system. For small values of , this situation leads to a boundary
layer, which is the main concern of this work. Our main result is that, under
appropriate regularity assumptions, and despite the presence of this boundary
layer, the solutions of the Euler- system converge, as ,
to the corresponding solution of the Euler equations, in in space,
uniformly in time. We also present an example involving parallel flows, in
order to illustrate the indifference to the boundary layer of the limit, which underlies our work.Comment: 22page
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 . 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 and
L^\infty((0,T)\times\o), where is independent of the viscosity, provided
that initial velocity is regular enough. Furthermore, rates of convergence are
obtained also.Comment: 45page
Actively implementing an evidence-based feeding guideline for critically ill patients (NEED): a multicenter, cluster-randomized, controlled trial
Background: Previous cluster-randomized controlled trials evaluating the impact of implementing evidence-based guidelines for nutrition therapy in critical illness do not consistently demonstrate patient benefits. A large-scale, sufficiently powered study is therefore warranted to ascertain the effects of guideline implementation on patient-centered outcomes.
Methods: We conducted a multicenter, cluster-randomized, parallel-controlled trial in intensive care units (ICUs) across China. We developed an evidence-based feeding guideline. ICUs randomly allocated to the guideline group formed a local "intervention team", which actively implemented the guideline using standardized educational materials, a graphical feeding protocol, and live online education outreach meetings conducted by members of the study management committee. ICUs assigned to the control group remained unaware of the guideline content. All ICUs enrolled patients who were expected to stay in the ICU longer than seven days. The primary outcome was all-cause mortality within 28 days of enrollment.
Results: Forty-eight ICUs were randomized to the guideline group and 49 to the control group. From March 2018 to July 2019, the guideline ICUs enrolled 1399 patients, and the control ICUs enrolled 1373 patients. Implementation of the guideline resulted in significantly earlier EN initiation (1.20 vs. 1.55 mean days to initiation of EN; difference − 0.40 [95% CI − 0.71 to − 0.09]; P = 0.01) and delayed PN initiation (1.29 vs. 0.80 mean days to start of PN; difference 1.06 [95% CI 0.44 to 1.67]; P = 0.001). There was no significant difference in 28-day mortality (14.2% vs. 15.2%; difference − 1.6% [95% CI − 4.3% to 1.2%]; P = 0.42) between groups.
Conclusions: In this large-scale, multicenter trial, active implementation of an evidence-based feeding guideline reduced the time to commencement of EN and overall PN use but did not translate to a reduction in mortality from critical illness. Trial registration: ISRCTN, ISRCTN12233792. Registered November 20th, 2017