Propriedades de soluções para as equações de Navier-Stokes, MHD e magneto-micropolares

• Autor(a) principal: Souza, Taynara Batista de
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFS
• Texto Completo: https://ri.ufs.br/handle/riufs/5825
• topic: Matemática; Equações de Navier-Stokes; Magnetoidrodinâmica; Espaços de Sobolev; Equações MHD; Equações magneto-micropolares; Explosão de solução; Navier-Stokes equations; MHD equations; Magneto-micropolar equations; Blow-up of solution; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we study blow-up results in finite time for the solution (u, b)(·, t) (defined in [0, T∗)), as well as for their spacial derivatives, of the Magnetohydrodynamic (MHD) system. These results are obtained by extending some statements found in the literature for the classical Navier- Stokes equations. In order to cite an example, we prove that k(u, b)(·, t)kq explodes at a rate (T∗ − t)−q−3 2q , for all t ∈ [0, T∗) and 3 < q < ∞. In addition, we prove some sufficient conditions for the existence of global solution (in time) for the Navier-Stokes and MHD equations. Finally, we generalize some results established from the MHD equations, involving Sobolev Spaces Homogeneous, to the Magneto-micropolar system. More precisely, we show that if the solution (u,w, b)(·, t) presents blow-up in T∗ < ∞, then k(u,w, b)(·, t)k ˙H sk(u,w, b)(·, t)k 2s 1+2 −1 2 ≥ C(T∗ − t) s 1+2 , for all t ∈ [0, T∗), where δ ∈ (0, 1) and s ≥ 1 2 + δ.