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Last Update: 16:52 - Wednesday - October 3rd 2018.


Next Seminar of 2018.2

A one million dollars problem from the point of view of continuation of solutions

Alexandre do Nascimento Oliveira Sousa

Doutorando - ICMC (USP)
In this work we consider the Navier-Stokes problem in $\mathbb{R}^N$: $$ \begin{array}{l} u_t=\Delta u - \nabla \pi + f(t) - (u\cdot \nabla) u, \quad x\in \Omega\\ \hbox{div}(u)=0,\quad x\in \Omega \\ u=0, \quad x\in \partial \Omega\\ u(0,x)=u_0(x), \end{array} $$ where $u_0\in L^N(\Omega)^N$ and $\Omega$ is a bounded open subset of $\mathbb{R}^N$ with smooth boundary. We prove that this problem is locally well posed and provide conditions to show that these solutions are defined for all $t\geq 0$. We offer an interpretation for the problem of the Clay Mathematics Institute concerning the Navier-Stokes equations.




Room: Room 202 - Maths Department       Date: Thursday - October 18th, 2018        Time: 14:00 to 15:00



Calendar for 2018.2

The lectures of the SED take place usually on Thursdays from 13:30 to 15:30 at Room 202 of the Maths Department building at UFSC.

Date Lecturer Institute Title
16/august Jáuber Cavalcante de Oliveira UFSC Existence and stability of time-periodic solutions of systems of PDEs including the Navier-Stokes equations
23/august - - -
30/august Paulo Antonio Liboni Filho UEL Palestra no Colóquio de Matemática*
6/september Matheus Cheque Bortolan UFSC Estimates for a nonautonomous wave equation in time-dependent spaces
13/september Cleverson Roberto da Luz UFSC Exact controllability of the wave equation with Dirichlet boundary condition
20/september Thales Maier de Souza UFSC - Joinville Asymptotic dynamics for a non-autonomous Navier-Stokes-Voigt equation
27/september - - -
4/october Ruy Coimbra Charão UFSC Decay rates of some $L^2$-norm for a generalized semilinear dissipative equation of Boussinesq/Plate type
11/october - - -
18/october Alexandre do Nascimento Oliveira Sousa Doutorando - ICMC (USP) A one million dollars problem from the point of view of continuation of solutions
25/october
1/november
8/november
15/november
22/november
29/november

About the Seminars

The SED is composed by weekly lectures, presented by researches on the fields of Differential Equations and Nonlinear Dynamical Systems, and its goal is to inform researchers and Math graduate students about the recent research developments on these areas.

Graduate Department



Head Chief: Prof. Marcelo Sobottka
E-mail: marcelo.sobottka at ufsc.br

First Assistant: Elisa Barbosa Amaral
E-mail: elisa.amaral at ufsc.br

Second Assistant: Érica Flores
E-mail: erica.flores at ufsc.br

Current Coordinator



Prof. Matheus Cheque Bortolan

E-mail: m.bortolan at ufsc.br
Home: mtm.ufsc.br/~bortolan
Phone: +55 (48) 3721-3699




Past Editions



2018:    1st Semester     2nd Semester   
2017:    1st Semester     2nd Semester   
2016:    1st Semester    2nd Semester
2015:    1st Semester    2nd Semester