Algebraic groups Seminar (Dipendra)

Date : Wednesday, 11 AM.

Venue:  Room 105

Host: Dipendra Prasad

speaker: Chayan Karmakar
Affiliation:  IIT Bombay

Title: Regular elements of semi-simple algebraic groups

Abstract: We will continue with the seminar on Algebraic groups by reading the paper of  Robert Steinberg, Regular elements of semi-simple algebraic Groups Publications mathématiques de l’I.H.É.S., tome 25 (1965), p. 49-80.

PDE-Seminar

Wednesday, 24 th  April 2024, 16:30 am-17:30 pm

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Venue: Ramanujan hall, Department of Mathematics, IIT Bombay

Host: Debanjana Mitra

Speaker: Dr. Dharmatti Sheetal

Affiliation: Department of Mathematics, IISER Thiruvananthapuram

Title:  Cahn-Hilliard-Navier-Stokes equations with Nonhomogeneous Boundary: Existence, Uniqueness, Regularity and Optimal Control
Abstract: The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes equations (CHNS System). In this work we study the well-posedness results for CHNS systems with nonhomogeneous boundary conditions for the velocity equation. We obtain the existence of global weak solutions in the two dimensional bounded domain using semi Galerkin approximation.  We further prove the continuous dependence of the solution on initial conditions and boundary data that will provide the uniqueness of the weak solution. The  existence of strong solutions is also established in this work. Furthermore, we study  optimal boundary control using the continuous dependance of strong solution. Using Pontryagin's maximum principle we show that the optimal control is characterised as a unique solution of the appropriate adjoint system.