Global existence of solutions to 2-D Navier-Stokes flow with non-decaying initial data in half-plane

We investigate the Navier-Stokes initial boundary value problem in the half-plane $R^2_+$ with initial data $u_0 \in L^\infty(R^2_+)\cap J_0^2(R^2_+)$ or with non decaying initial data $u_0\in L^\infty(R^2_+) \cap J_0^p(R^2_+), p > 2$ . We introduce a technique that allows to solve the two-dimesional problem, further, but not least, it can be also employed to obtain weak solutions, as regards the non decaying initial data, to the three-dimensional Navier-Stokes IBVP. This last result is the first of its kind

Homogenization of oxygen transport in biological tissues

In this paper, we extend previous work on the mathematical modeling of oxygen transport in biological tissues (Matzavinos et al., 2009). Specifically, we include in the modeling process the arterial and venous microstructure within the tissue by means of homogenization techniques. We focus on the two-layer tissue architecture investigated in (Matzavinos et al., 2009) in the context of abdominal tissue flaps that are commonly used for reconstructive surgery. We apply two-scale convergence methods and unfolding operator techniques to homogenize the developed microscopic model, which involves different unit-cell geometries in the two distinct tissue layers (skin layer and fat tissue) to account for different arterial branching patterns

The Stokes and Poisson problem in variable exponent spaces

We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove the existence of strong and weak solutions for bounded domains with C^{1,1} boundary with inhomogenous boundary values. The result is based on generalizations of the classical theories of Calderon-Zygmund and Agmon-Douglis-Nirenberg to variable exponent spaces.Comment: 20 pages, 1 figur

Horizontal Approximate Deconvolution for Stratified Flows: Analysis and Computations

In this paper we propose a new Large Eddy Simulation model derived by approximate deconvolution obtained by means of wave-number asymptotic expansions. This LES model is designed for oceanic flows and in particular to simulate mixing of fluids with different temperatures, density or salinity. The model -which exploits some ideas well diffused in the community- is based on a suitable horizontal filtering of the equations. We prove a couple of a-priori estimates, showing certain mathematical properties and we present also the results of some preliminary numerical experiments

What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations—e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being “suboptimal”. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significantly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the “neural code”. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neuroscientists and biologists, both computational and experimental, to embrace a very broad definition of stochastic resonance in terms of signal-processing “noise benefits”, and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology

An Introduction to the Mathematical Theory of the Navier-Stokes Equations

The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994. In this new edition, the two volumes have merged into one and two more chapters on steady generalized os

On the Stability of Steady-State Solutions to the Navier-Stokes Equations in the Whole Space

We prove asymptotic stability of steady-state solutions to the Navier-Stokes equations in the whole space. One of the novelties of this work consists in considering perturbations that show a distinct pointwise behavior (in space and time) and correspond to initial data only belonging to suitable weighted Lebesgue spaces