Description

Mathematics Colloquium Date and time: 14 September 2022 at 4 pm Venue: Ramanujan Hall (Room 213, II Floor) Title: Boundary null-controllability of 1d linearized compressible Navier-Stokes System by one control force. Speaker: Shirshendu Chowdhury, Department of Mathematics and Statistics, IISER Kolkata, Abstract: In the first part of the talk, we introduce the concept of controllability of Differential Equations. Then we give some examples in finite (ODE) and infinite dimensional(PDE) contexts. We recall the controllability results of the Transport and Heat equation. In the second part of the talk, 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 >0 $. It is a Coupled system of transport and heat type equations. We study the boundary null-controllability of this linearized system in the interval $(0,1)$ when a Dirichlet control function is acting either only on the density or only on the velocity component at one end of the interval. We obtain null controllability using one boundary control in the space ${H}^s_{per}(0,1)\times L^2(0,1)$ for any $s>\frac{1}{2}$ provided the time $T>1$, where ${H}_{per}^s(0,1)$ denotes the Sobolev space of periodic functions. The proof is based on spectral analysis and on solving a mixed parabolic-hyperbolic moments problem and a parabolic hyperbolic joint Ingham-type inequality. This is a recent joint work (https://arxiv.org/abs/2204.02375 [1], 2022) with Kuntal Bhandari, Rajib Dutta and Jiten Kumbhakar. Note: Mathematics Colloquia are accessible to the general audience Links: ------ [1] https://arxiv.org/abs/2204.02375

Description

Ramanujan Hall, Department of Mathematics

URL

Ramanujan Hall, Department of Mathematics

Date

Wed, September 14, 2022

Start Time

4:00pm-5:00pm IST

Duration

1 hour

Priority

5-Medium

Access

Public

Created by

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Updated

Tue, September 13, 2022 1:52pm IST