Search results for "102"
showing 10 items of 2892 documents
Zero Viscosity Limit for Analytic Solutions of the Primitive Equations
2016
The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be \({O(\sqrt{\nu})}\). The main assumption is spatial analyticity of the initial datum.
The Navier–Stokes equations in exterior Lipschitz domains: L -theory
2020
Abstract We show that the Stokes operator defined on L σ p ( Ω ) for an exterior Lipschitz domain Ω ⊂ R n ( n ≥ 3 ) admits maximal regularity provided that p satisfies | 1 / p − 1 / 2 | 1 / ( 2 n ) + e for some e > 0 . In particular, we prove that the negative of the Stokes operator generates a bounded analytic semigroup on L σ p ( Ω ) for such p. In addition, L p - L q -mapping properties of the Stokes semigroup and its gradient with optimal decay estimates are obtained. This enables us to prove the existence of mild solutions to the Navier–Stokes equations in the critical space L ∞ ( 0 , T ; L σ 3 ( Ω ) ) (locally in time and globally in time for small initial data).
An odor timer in milk? Synchrony in the odor of milk effluvium and neonatal chemosensation in the mouse.
2012
International audience; Mammalian newborns exhibit avid responsiveness to odor compounds emanating from conspecific milk. Milk is however developmentally heterogeneous in composition as a function of both evolved constraints and offspring demand. The present study aimed to verify whether milk odor attractivity for neonates is equally distributed along lactation in Mus musculus (Balb-c strain). Therefore, we exposed pups varying in age to milk samples collected from females in different lactational stages. The pups were assayed at postnatal days 2 (P2), 6 (P6) and 15 (P15) in a series of paired-choice tests opposing either murine milk and a blank (water), or two samples of milk collected in …
Use of running plates by floor housed rats: A pilot study
2021
The outfit of husbandry facilities of, and the enrichment provided for, experimental rodents plays an important role in the animals’ welfare, and hence also for the societal acceptance of animal experiments. Whether rats and mice benefit from being provided with running wheels or plates is discussed controversially. Here we present observations from a feeding experiment, where rats were provided a running plate. As a pilot study, six identical cages, with three animals per cage, were filmed for six days, and the resulting footage was screened for the number of bouts and the time the animals spent on the plates. The main activities observed on the plate in descending order were sitting (18.…
Untargeted Antifungal Treatment in the ICU: Changing Definitions and Labels Do Not Change the Evidence.
2018
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New indefinite integrals from a method using Riccati equations
2018
ABSTRACTAn earlier method for obtaining indefinite integrals of special function from the second-order linear equations which define them has been reformulated in terms of Riccati equations, which ...
Themes within lecturers' views on the teaching of linear algebra
2019
Author's accepted manuscript (postprint). This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Mathematical Education in Science and Technology on 25/09/2019, available online: http://www.tandfonline.com/10.1080/0020739X.2019.1668976. Available from 26/09/2020. This paper reports on themes that arose in an investigation of university lecturers’ views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course? Are there tools that should/should not …
Multiple normalized solutions for a Sobolev critical Schrödinger-Poisson-Slater equation
2021
We look for solutions to the Schr\"{o}dinger-Poisson-Slater equation $$- \Delta u + \lambda u - \gamma (|x|^{-1} * |u|^2) u - a |u|^{p-2}u = 0 \quad \text{in} \quad \mathbb{R}^3, $$ which satisfy \begin{equation*} \int_{\mathbb{R}^3}|u|^2 \, dx = c \end{equation*} for some prescribed $c>0$. Here $ u \in H^1(\mathbb{R}^3)$, $\gamma \in \mathbb{R},$ $ a \in \mathbb{R}$ and $p \in (\frac{10}{3}, 6]$. When $\gamma >0$ and $a > 0$, both in the Sobolev subcritical case $p \in (\frac{10}{3}, 6)$ and in the Sobolev critical case $p=6$, we show that there exists a $c_1>0$ such that, for any $c \in (0,c_1)$, the equation admits two solutions $u_c^+$ and $u_c^-$ which can be characterized respectively…
Some perturbation results through localized SVEP
2016
Some classical perturbation results on Fredholm theory are proved and extended by using the stability of the localized single-valued extension property under Riesz commuting perturbations. In the last part, we give some results concerning the stability of property (gR) and property (gb.
Lipschitz-type conditions on homogeneous Banach spaces of analytic functions
2017
Abstract In this paper we deal with Banach spaces of analytic functions X defined on the unit disk satisfying that R t f ∈ X for any t > 0 and f ∈ X , where R t f ( z ) = f ( e i t z ) . We study the space of functions in X such that ‖ P r ( D f ) ‖ X = O ( ω ( 1 − r ) 1 − r ) , r → 1 − where D f ( z ) = ∑ n = 0 ∞ ( n + 1 ) a n z n and ω is a continuous and non-decreasing weight satisfying certain mild assumptions. The space under consideration is shown to coincide with the subspace of functions in X satisfying any of the following conditions: (a) ‖ R t f − f ‖ X = O ( ω ( t ) ) , (b) ‖ P r f − f ‖ X = O ( ω ( 1 − r ) ) , (c) ‖ Δ n f ‖ X = O ( ω ( 2 − n ) ) , or (d) ‖ f − s n f ‖ X = O ( ω …