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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