instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Existence and uniqueness for the Ladyzhenskaya model of incompressible viscous fluid and one introduction of the pullback attractors
Seminario PHD
 Date: 19.02.2019 16.30 Venue: Seminario I (IMUS), Edificio Celestino Mutis Author: Heraclio Ledgar López Lázaro Organization: Moisés Rodríguez Madrena Cristina Caravaca García Tanausú Aguilar Hernández Marina Leal Palazón
we establish a result of existence (global in time) and uniqueness of solution for the Ladyzhenskaya model of incompressible viscous fluid in a domain $\Omega\subset{\mathbb{R}}^{n}$, $n\geq2$. The motion of incompressible, viscous fluids in $\Omega$, characterized by the velocity field $u=(u_{1},...,u_{n})$ and the pressure $\pi$, is governed by the system of $n+1$ equations

\left\{\begin{array}{l}
\frac{\partial u}{\partial t}-div_{x}S(Du)+div_{x}(u\otimes u)+\nabla_{x}\pi=f\;\;in\;(\tau,+\infty)\times\Omega,\\
div_{x}u=0\;\;in\;(\tau,+\infty)\times\Omega,\\
u(\tau,x)=u_{\tau}(x),\;\;x\in\Omega,\\
u=0\;\;on\;(\tau,+\infty)\times\partial\Omega,
\end{array}\right.

where the operator $S$ is a potential. If we have time, we will make some comments on the long-time behavior.

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