Discussion Meeting on Equations of Fluid Models : Control, Homogenization and Numeric

Schedule

Speakers

Dr Dharmatti Sheetal ( IISER Thiruvananthapuram )

> Title: Optimal control problems for Cahn Hilliard Navier Stokes' system

> Abstract:

Dr Muthukumar T ( IIT Kanpur )

> Title: Parabolic problem on an Evolving domain with rapidly oscillating boundary

> Abstract: In this talk, we shall motivate the need to study the problem in an evolving (moving) domain from the fluid-structure interaction perspective. We shall introduce the intrinsic difficulties of the problem with Navier-Stokes equation and explore how it is important to un-derstand the corresponding problems in Parabolic and Stokes system. Then a possible approach to parabolic problems will be presented.

Dr Bidhan Chandra (IIT Kanpur)

> Title: Homogenization of Steady Stokes Problem in an Oscillating Domain

> Abstract: We introduce the steady Stokes system in a n-dimensional domain Ωε with Neumann type boundary condition on the oscillating part of the boundary. Our aim is to study the limiting analysis (as E → 0) of the steady Stokes problem and identify the limit problem in a fixed domain. Finally, show the corrector results.

Mr Shankar ( IIT Kanpur)

> Title: Non-stationary Stokes system on an Evolving domain with highly oscillating boundary

> Abstract: In this talk, we discuss the existence, uniqueness of solution to the non-stationary Stokes system in a domain with highly oscillating (time-dependent) boundary and an inhomogeneous time-dependent data on the oscillating part of boundary.

Prof Thirupathi Gudi ( IISc Bangalore )

> Title: Edge Patch-wise Local Projection Stabilizing FE Methods for Oseen Problem

> Abstract: Oseen problem is the linearized version of the Navier-Stokes problem that appears in fluid flow models. The Oseen equation is a convection-diffusion problem where the convection may be dominant.
The standard finite element methods for this problem fail to provide a stable non oscillatory solution. Due to the enormous applications, It is important to construct stabilized methods which suppress the oscillations and provide a stable numerical solution for this problem. The Local Projection Stabilizing technique is a popular method in this context. We propose and analyze edge-patch wise local projection stabilizing nonconforming finite element methods and illustrate with numerical experiments.

This is a joint work with Asha K. Dond and Rahul Biswas.

Dr Shirshendu Chowdhury ( IISER Kolkata )

> Title: Null controllability of the incompressible Navier-Stokes equations in a 2-D channel using normal boundary control

Sza ́sz Theore> Abstract: We consider the Stokes equations in a two-dimensional channel with periodic conditions in the direction of the channel. We establish null controllability of this system using a boundary control which acts on the normal component of the velocity only. We show null controllability of the system, subject to a constraint of zero average, by proving an observability inequality with the help of a Mu ̈ntz-m.

This is a joint work with Michael Renardy and Debanjana Mitra.

Prof Mythily Ramaswamy ( TIFR CAM, Bangalore )

> Title: Local stabilization of Boussinesq System

> Abstract: We consider Boussinesq system in a two dimensional polygonal domain with mixed boundary conditions. After determining the precise loss of regularity due to corners and mixed boundary conditions, we set up a suitable function framework to study the system and prove its stabilizability. Finally we construct a finite dimensional feedback and show it stabilizes the nonlinear system locally.

Dr Debanajana Mitra ( IIT Bombay )

> Title: Control of visco-elastic fluid models

> Abstract:My talk will be devoted to study the control of linear visco-elastic flows- Jeffreys model and Maxwell model. We mainly use spectral characterization of the operator associated to the linearized PDE and Fourier series techniques to prove controllability results. Further, microlocal analysis is used to prove the lack of null controllability of the systems. How the hyperbolic and parabolic behaviors of equations effect the controllability of equations will be indicated.