Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-02-27Bitstream added on 2014-06-13T19:27:07Z : No. of bitstreams: 1 lopes_jh_me_sjrp.pdf: 490230 bytes, checksum: f1439f3747d9808ad9df33bfcbfc16d3 (MD5) / Neste trabalho, estudaremos as equações de Navier-Stokes em Rn e mostraremos a existência de solução global, quando a velocidade inicial u0(x) pertence ao espaço Lp-fraco e tem norma suficientemente pequena. A análise da evolução da solução é realizada em espaços funcionais de Kato-Fujita, invariantes pelo scaling de Navier-Stokes. Mostraremos também que se u0(x) é homogênea de grau −1, as soluções também são invariantes por este scaling, ou seja, elas são auto-similares. Além disso, mostraremos a estabilidade assintótica das soluções mild / In this work, we study the Navier-Stokes equations in Rn and show the existence of global solution, when the initial velocity u0(x) belongs to weak Lp space with a sufficiently small norm. The evolution of the solution is analyzed in function spaces with Kato-Fujita type norms invariant by scaling of Navier-Stokes. We also show that if u0 is an homogeneous function of degree −1, the solutions are also invariant by that scaling, i.e., they are self-similar. Moreover, we show the asymptotic stability of mild solutions

Orientador: Juliana Conceição Precioso Pereira / Banca: Lucas Catão de Freitas Ferreira / Banca: Andréa Cristina Prokopczyk Arita / Resumo: Neste trabalho, estudaremos as equações de Navier-Stokes em Rn e mostraremos a existência de solução global, quando a velocidade inicial u0(x) pertence ao espaço Lp-fraco e tem norma suficientemente pequena. A análise da evolução da solução é realizada em espaços funcionais de Kato-Fujita, invariantes pelo scaling de Navier-Stokes. Mostraremos também que se u0(x) é homogênea de grau −1, as soluções também são invariantes por este scaling, ou seja, elas são auto-similares. Além disso, mostraremos a estabilidade assintótica das soluções mild / Abstract: In this work, we study the Navier-Stokes equations in Rn and show the existence of global solution, when the initial velocity u0(x) belongs to weak Lp space with a sufficiently small norm. The evolution of the solution is analyzed in function spaces with Kato-Fujita type norms invariant by scaling of Navier-Stokes. We also show that if u0 is an homogeneous function of degree −1, the solutions are also invariant by that scaling, i.e., they are self-similar. Moreover, we show the asymptotic stability of mild solutions / Mestre

A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.

This thesis considered the connections between parabolic partial differential equations of the diffusion type and Gaussian-Markov stochastic processes, in particular the Wiener process. A method has been developed by which certain Wiener integrals of the type∫C0[0,1] exp{t/a ∫1/0 e[t(1-s), 2 √(t/a) x(s) =ξ] ds} o [2√(t/a) x(1) – ξ] dwxHave been obtained as solutions of non-homogeneous heat equations. In the appendix the method has been extended to the evaluation of Wiener integrals of the type,∫C0 [0,t] exp {∫t/0 e [t-s, x(s) + ξ] ds} o [x(s) + ξ] dwx.In addition an inequality which gives bounds for Wiener integrals of the type∫C0 [s,t] exp {-∫t/s F[x( r )] dr} dwx has been deduced.Further, certain parabolic partial differential equations have been solved by building suitable Green’s functions through Gaussian-Markov stochastic processes. Two stochastic processes which exhibit certain interesting features have been obtained and briefly discussed.Ball State UniversityMuncie, IN 47306

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 95-97). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1999. / Typescript. Vita. Includes bibliographical references (leaves 95-97). Also available on the Internet.

Thesis (M.S.)--Mississippi State University. Department of Computational Engineering. / Title from title screen. Includes bibliographical references.

Thesis (M.S.)--Mississippi State University. Department of Computational Engineering. / Title from title screen. Includes bibliographical references.

Not available / text

In this thesis, we consider soltions to the two-dimensional Euler equations with uniformly continuous initial vorticity in a critical or subcritical Besov space. We use paradifferential calculus to show that the solution will lose an arbitrarily small amount of smoothness over any fixed finite time interval. This result is motivated by a theorem of Bahouri and Chemin which states that the Sobolev exponent of a solution to the two-dimensional Euler equations in a critical or subcritical Sobolev space may decay exponentially with time. To prove our result, one can use methods similar to those used by Bahouri and Chemin for initial vorticity in a Besov space with Besov exponent between 0 and 1; however, we use different methods to prove a result which applies for any Sobolev exponent between 0 and 2. The remainder of this thesis is based on joint work with J. Kelliher. We study the vanishing viscosity limit of solutions of the Navier-Stokes equations to solutions of the Euler equations in the plane assuming initial vorticity is in a variant Besov space introduced by Vishik. Our methods allow us to extend a global in time uniqueness result established by Vishik for the two-dimensional Euler equations in this space. / text