Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

Finite time blow-up and breaking of solitary wind waves

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.

Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Sliding Vector Fields via Slow-Fast Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Study of Singularities in Nonsmooth Dynamical Systems via Singular Perturbation

In this article we describe some qualitative and geometric aspects of nonsmooth dynamical systems theory around typical singularities. We also establish an interaction between nonsmooth systems and geometric singular perturbation theory. Such systems are represented by discontinuous vector fields on R(l), l >= 2, where their discontinuity set is a codimension one algebraic variety. By means of a regularization process proceeded by a blow-up technique we are able to bring about some results that bridge the space between discontinuous systems and singularly perturbed smooth systems. We also present an analysis of a subclass of discontinuous vector fields that present transient behavior in the 2-dimensional case, and we dedicate a section to providing sufficient conditions in order for our systems to have local asymptotic stability.

Um estudo de bifurcações de codimensão dois de campos de vetores

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Um estudo global de campos de vetores planares

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cloning, sequencing and expression analysis of the equine hepcidin gene by real-time PCR

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Lipopolysaccharide infusion up-regulates hepcidin mRNA expression in equine liver

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exact Foldy-Wouthuysen transformation for real spin-0 particle in curved space

Up to now, the only known exact Foldy-Wouthuysen transformation (FWT) in curved space is that concerning Dirac particles coupled to static spacetime metrics. Here we construct the exact FWT related to a real spin-0 particle for the aforementioned spacetimes. This exact transformation exists independently of the value of the coupling between the scalar field and gravity. Moreover, the gravitational Darwin term written for the conformal coupling is one-third of the corresponding term in the fermionic case. There are some arguments in the literature that seem to favor the choice lambda=1/6. We rehearse a number of claims of these works.

Genetic Algorithms (Binary and Real Codes) for the Optimisation of a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A construção teórica do real: Uma questão para a produção do conhecimento em educação

The central theme of this article is the research in education. The aim is to bring up the contribution developed by Mirian Limoeiro Cardoso in Brazil for the production of knowledge in education, besides the propositions of foreign authors, often used as references to base of the research. The starting point, here described, is the statement that the empirical real is not the object of knowledge, but what is presented as an object to be known, is always the real that, in different forms, is an object involved by theory. Thinking about the research in this view the necessecity of revision of the meaning of the object to be known, the object that is also an educative action in its different and several manifestations and the discussion of its importance for the teachers? and researchers? formation.

Entre o formal e o real: representações acerca do modelo disciplinar da Fundação CASA de Araraquara

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Pequenas criaturas e o efeito de real: a estética da crueldade em Rubem Fonseca

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Enumeração celular pela quantificação absoluta por PCR em tempo real de culturas de bradirrizóbios

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)