Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time variable.Comment: 14 pages, to appea

Qualidade do leite na bacia leiteira de Castanhal: resultados de pesquisas e recomendações.

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Qualidade do leite nas propriedades do município de Uruará, Pará.

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Processamento do leite na microrregião de Castanhal e Município de Uruará.

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Equilibrium analysis of an immersed rigid leaflet by the virtual element method

We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the properties of the domain functional describing the angular momentum exerted by the fluid on the leaflet (which depends on both the leaflet angular position and its thickness), we identify sufficient conditions on the spring stiffness function for the existence (and uniqueness) of equilibrium positions. This study resorts to techniques from shape differential calculus. We propose a numerical technique that exploits the mesh flexibility of the Virtual Element Method (VEM). A (polygonal) computational mesh is generated by cutting a fixed background grid with the leaflet geometry, and the problem is then solved with stable VEM Stokes elements of degrees 1 and 2 combined with a bisection algorithm. We prove quasi-optimal error estimates and present a large array of numerical experiments to document the accuracy and robustness with respect to degenerate geometry of the proposed methodology

Projeto SENSOR: políticas públicas relacionadas a expansão da Cana-de-açúcar para a produção de biocombustíveis.

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On the regularity up to the boundary for certain nonlinear elliptic systems

We consider a class of nonlinear elliptic systems and we prove regularity up to the boundary for second order derivatives. In the proof we trace carefully the dependence on the various parameters of the problem, in order to establish, in a further work, results for more general systems