Global Well-posedness And Symmetries For Dissipative Active Scalar Equations With Positive-order Couplings

We consider a family of dissipative active scalar equations outside the L-2-space. This was introduced in [7] and its velocity fields are coupled with the active scalar via a class of multiplier operators which morally behave as derivatives of positive order. We prove global well-posedness and time-decay of solutions, without smallness assumptions, for initial data belonging to the critical Lebesgue space Ln/2 gamma-beta(R-n) which is a class larger than that of the above reference. Symmetry properties of solutions are investigated depending on the symmetry of initial data and coupling operators.6052555

ON THE STABILITY PROBLEM FOR THE BOUSSINESQ EQUATIONS IN WEAK-L-p SPACES

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We consider the Boussinesq equations in either an exterior domain in R-n, the whole space R-n, the half space R-+(n) or a bounded domain in R-n, where the dimension n satisfies n >= 3. We give a class of stable steady solutions, which improves and complements the previous stability results. Our results give a complete answer to the stability problem for the Boussinesq equations in weak-L-p spaces, in the sense that we only assume that the stable steady solution belongs to scaling invariant class L-sigma((n, infinity)) x L-(n,L- infinity). Moreover, some considerations about the exponential decay (in bounded domains) and the uniqueness of the disturbance are done.93667684Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Formação do eu professor na abordagem Walloniana*

RESUMO Objetivos Analisar como o professor percebe a construção de seu Eu Professor na perspectiva de Wallon e conhecer como vivencia seu cotidiano na escola na condição de ser o si mesmo e o outro. Método Estudo qualitativo que contou com 13 participantes atuantes no Curso Bacharelado em Enfermagem. A coleta de dados foi realizada em 2013, por meio de entrevistas submetidas à análise temática. Resultados Emergiram três categorias: Construção do Eu Professor; Viver o cotidiano apoiado em si mesmo e no outro; e Componentes da construção do Eu Professor, com destaque para a conscientização e valorização de si mesmo e do outro, edificando a construção do Eu Professor. Conclusão Os professores percorreram uma trajetória na qual permitiu reconhecer o si mesmo em diferentes movimentos da internalização do Eu

ON THE UNIQUENESS FOR SUB-CRITICAL QUASI-GEOSTROPHIC EQUATIONS

We prove uniqueness of mild solutions in the class C([0,Tau); L(n/2 gamma-1)) 0<Tau <=infinity, for sub-critical quasi-geostrophic equations without assuming any smallness condition. As a consequence, any mild solution in C([0,infinity); L(2/2 gamma-1)) satisfies the regularity and decay properties given in the previous paper [4]. The proof is performed in the framework of Lorentz spaces.91576

Existence and scattering theory for Boussinesq type equations with singular data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We study the initial value problem for the generalized Boussinesq equation and prove existence of local and global solutions with singular initial data in weak-L(P) spaces. Our class of initial data for global existence is larger than that of Cho and Ozawa (2007) [7]. Long time behavior results are obtained and a scattering theory is proved in that framework. With more structure, we show Sobolev H(1) and Lorentz-type L((p,q)) regularity properties for the obtained solutions. The approach employed is unified for all dimensions n >= 1. (C) 2010 Elsevier Inc. All rights reserved.250523722388Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

A family of dissipative active scalar equations with singular velocity and measure initial data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This paper considers a family of generalized active scalar equations, with fractional dissipation, whose velocity fields are more singular than Riesz transform. We prove global well-posedness results for small initial data belonging to Besov-Morrey spaces, which contain strongly singular functions and measures concentrated at points (Diracs) and on smooth curves. Self-similar solutions are obtained for initial data and coupling-velocity operator with correct homogeneities. We also show an asymptotic behavior result and obtain a class of asymptotically self-similar solutions. (C) 2012 Elsevier Ltd. All rights reserved.6410SI32923301Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq