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Submitted by sde on 21 March, 2015 - 19:06

Date/Time:

Friday, April 10, 2015 -

16:00 to 17:00

Venue:

LH-105

Speaker:

Dr. Shirshendu Chowdhury

Affiliation:

TIFR-CAM, Bangalore

Title:

Controllability of Linearized Compressible Navier Stokes equations

Abstract: We will describe: (i) What is Controllability problem (ii) Examples and known results: ODE (finite dim), transport equation, Heat equation (infinite dim ). Then we consider compressible Navier-Stokes equations in one dimension, linearized around a constant steady state $(Q_0,V_0)$, with $Q_0 > 0,V_0\geq 0$. It is a coupled system involving both transport and parabolic effects. We study the controllability of this linearized system in bounded interval $(0,L)$. We find that the properties of the two semigroups $(e^{tA})_{t\geq0} $ (the one when $V_0 = 0$ and the one when $V_0> 0$) and the spectrum of $A$ are completely different where $A$ is the corresponding linearized operator. We obtain several interesting positive and negative results for the null controllability and approximate controllability of the system using interior or boundary control in both the cases $V_0 =0$ and $V_0>0$.

**School of Mathematical Sciences**

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