Search results for "General Mathematics"
showing 10 items of 3795 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).
Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular freq…
1995
If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper. In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II. Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as—if the equations are viewed as a three-dimensional dynamical system—the unique stable equilibrium, which depends on the spin. This equilibri…
Chaotic dynamics and partial hyperbolicity
2017
The dynamics of hyperbolic systems is considered well understood from topological point of view as well as from stochastic point of view. S. Smale and R. Abraham gave an example showing that, in general, the hyperbolic systems are not dense among all differentiable systems. In 1970s, M. Brin and Y. Pesin proposed a new notion: partial hyperbolicity to release the notion of hyperbolicity. One aim of this thesis is to understand the dynamics of certain partially hyperbolic systems from stochastic point of view as well as from topological point of view. From stochastic point of view, we prove the following results: — There exists an open and dense subset U of robustly transitive nonhyperbolic …
Untargeted Antifungal Treatment in the ICU: Changing Definitions and Labels Do Not Change the Evidence.
2018
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Tres textos en diálogo con la teoría del análisis didáctico de Luis Rico
2016
En este monográfico, presentamos tres textos que, con motivo de la jubilación del profesor Luis Rico, dialogan con su concepto de “análisis didáctico”. En las teorías, los términos propios de ellas suelen estar definidos para perfilar su significado, en especial cuando se está usando un término que ya tiene un campo semántico más o menos grande en su uso civil o en otras teorías, como es el caso de “análisis” y de “didáctico”. En el caso de los términos propios de las teorías puede pues relajarse la consideración de que el significado está en el uso y quedarse uno con lo que diga la definición que da quien elabora la teoría –en todo caso, la definición explícita es uno de los lugares en que…
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.