NCMW - Mathematical Analysis of Fluid Flow Models (2024)

Speakers and Syllabus

 Syllabus to be covered in terms of modules of 6 lectures each:

Name of the  speakers with their affiliation. No. of Lectur es Detailed Syllabus
Prof. Mythily Ramaswamy
(ICTS-TIFR)		 6 Derivations of fluid equations and spaces of hydrodynamics: Lagrangian and Eulerian descriptions of the flow, transport theorem, inviscid and viscous fluids, energy equations.
Dr. Rajib Dutta
(IISER-Kolkata)		 6 Linear parabolic equations: Time dependent Sobolev spaces, Sobolev inequalities and compactness theorems, concept of weak solutions, existence and uniqueness of weak solutions,
Dr. Shirshendu Chowdhury
(IISER-Kolkata)		 6 Spaces of hydrodynamics, Helmholtz decomposition, Leray projection and De Rham’s theorem. Stokes equation: Well-posedness of the steady Stokes problem, Stokes operator and its properties.
Dr. Debanjana Mitra
(IIT-Bombay)		 6 Weak solutions of the unsteady Stokes equation. Regularity of weak solutions. Strong solutions for heat and Stokes equation. Maximal regularity.
Dr. Debayan Maity
(TIFR-CAM)		 6 Existence and uniqueness of local in time strong solutions, global existence in two dimension, small data global existence in three dimension. Vanishing viscosity limit.
Prof. Ujjwal Koley
(TIFR-CAM)		 6 Weak solutions to incompressible Navier-Stokes equations: Existence of Leray- Hopf weak solutions in Rn, n = 2,3. Uniqueness and regularity of weak solutions in n = 2, 3, Prodi-Serrin condition.

References:

  1. J. Bedrossian and V. Vicol, The mathematical analysis of the incompressible Euler and Navier-Stokes equations. An introduction, vol. 225 of Grad. Stud. Math., Providence, RI: American Mathematical Society (AMS), 2022.
  2. F. Boyer and P. Fabrie, Mathematical tools for the study of the incompressible Navier-Stokes equations and related models, Applied Mathematical Sciences, 183. Springer, New York, 2013.
  3. G. P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I, 1994. Linearized steady problems.
  4. P. G. Lemarié-Rieusset, Recent developments in the Navier-Stokes problem, Chapman & Hall/ CRC Research Notes in Mathematics, vol. 431, Chapman & Hall/CRC, Boca Raton, FL, 2002
  5. J. C. Robinson, J. L. Rodrigo, W. Sadowski, The three-dimensional Navier- Stokes equations, Classical theory, Cambridge Studies in Advanced Mathematics, vol. 157, Cambridge University Press,Cambridge, 2016.
  6. 6. R. Temam, Navier-Stokes equations. Theory and numerical analysis. Revised edition. With an appendix by F. Thomasset, Studies in Mathematics and its Applications, 2. North-Holland Publishing Co., Amsterdam- New York.

(Lecture notes from the speakers, if available)
Names of the tutors with their affiliation :

  1. Anupam Nayak (TIFR CAM)
  2. Keshav Sharma (TIFR CAM)
  3. Vaibhav Jena (TIFR CAM)
  4. Kush Kinra (TIFR CAM)

Time Table

 Week1

Day Date Lecture 1
(9.30– 11.00) 		Tea
(11.0 5– 11.25 ) 		Lecture 2
(11.30– 1.00) 		Lunch
(1.05–1.55) 		Lecture 3
(2.00–3.30) 		Tea
(3.35- 3.55)		 Discussion
(4.00-5.0 0) 		Snacks
5.05-5.35
    (name of the speaker)   (name of the speaker)   (name of the speaker)   (Name of the tutor)  
Mon 10/06/24 MR   RD   SC   MR + VJ+ KK  
Tues 11/06/24 MR   RD   SC   RD + VJ+ KK  
Wed 12/06/24 MR   RD   SC   SC+ VJ+ KK  
Thu 13/06/24 MR   RD   SC   MR+ VJ+ KK  
Fri 14/06/24 MR   RD   SC   RD+ VJ+ KK  
Sat 15/06/24 MR   RD   SC   SC+ VJ+ KK  

 

Week2

Day Date Lecture 1
(9.30– 11.00)		 Tea
(11.05– 11.25)		 Lecture 2
(11.30– 1.00)		 Lunch
(1.05– 1.55)		 Lecture 3
(2.00– 3.30)		 Tea
(3.35-3 .55)		 Discussion
(4.00-5.00 )		 Snacks
5.05-5 .35
    (name of the speaker)   (name of the speaker)   (name of the speaker)   (Name of the tutor)  
Mon 17/06/24 UK   DMi   DM   UK + AN+KS  
Tues 18/06/24 UK   DMi   DM   DMi + AN+KS  
Wed 19/06/24 UK   DMi   DM   DM + AN+KS  
Thu 20/06/24 UK   DMi   DM   UK + AN+KS  
Fri 21/06/24 UK   DMi   DM   DMi + AN+KS  
Sat 22/06/24 UK   DMi   DM   DM + AN+KS  

 

Full forms for the abbreviations of speakers and tutors:

Speakers :

MR - Mythily Ramaswamy
RD - Rajib Dutta
SC - Shirshendu Chowdhury
UK - Ujjwal Koley
DMi - Debanjana Mitra
DM - Debayan Maity

Tutors:

KS - Keshav Sharma
AN - Anupam Nayak
VJ - Vaibhav Jena
KK - Kush Kinra

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