Mathematical Analysis of Fluid Flow Models (2024)

Convener(s)

 
Name:  Prof. Ujjwal Koley Dr. Debayan Maity
Mailing Address:

Associate Professor
TIFR Centre for Applicable Mathematics,
Sharada Nagar,Yelahanka New Town,
Bengaluru, 560065.

 Assistant Professor
TIFR Centre for Applicable Mathematics,
Sharada Nagar,Yelahanka New Town,
Bengaluru, 560065.
Email:   ujjwal at math.tifrbng.res.in debayan at tifrbng.res.in

This NCM workshop aims to introduce the participants to the mathematical analysis of fluid flow equations. This will be extremely beneficial to both young researchers who want to pursue research in the field of mathematical fluid mechanics and those who are already working in the related areas. Our plan is to start from the scratch and develop the theory without assuming any background knowledge on fluid mechanics. Anyone with a basic knowledge of measure theory and functional analysis will be able to easily follow the lectures.
To be more specific, we intend to start with detailed derivations of fluid flow equations, introduce spaces of hydrodynamics, and then establish weak, and strong solutions for heat and Stokes equations, during the first week. During the second week our focus will be on incompressible Navier-Stokes equations. We plan to talk about Leray-Hopf weak solutions and their properties for incompressible Navier-Stokes equations, and existence and uniqueness of strong solutions to Navier-Stokes equations

Dates: 

Monday, June 10, 2024 - 19:00 to Saturday, June 22, 2024 - 19:00

Venue: 

Venue Address: 

 TIFR Centre for Applicable Mathematics, Sharada Nagar, Yelahanka New
Town, Bengaluru, 560065

 

 

 

Venue State: 

Venue City: 

PIN: 

560065

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

Selected Applicants: 

 

 

Sr.n SID Full Name Gender Affiliation Position in College/University University/ Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 55083 Mr. Sangram Satpathi Male IISER-TVM IPhD IISER TVM    
2 55126 Mr Jeyaponsankar P Male Bharathiar University. Research scholar(PhD) St.Joseph's college,Tiruchirappalli. 2021  
3 55160 Mr. Rohan Manish Didmishe Male Indian Institute of Science Education and Research, Kolkata Int. BS-MS Indian Institute of Science Education and Research, Kolkata Appeared  
4 55455 Mr. Navaneethakrishnan V Male Bharathiar University PhD M. Sc. Mathematics 2021  
5 55493 Mr. Saroj Si Male IIT Roorkee PhD Utkal University, Vanivihar, Odisha 2018  
6 55503 Mr. Jiten Kumbhakar Male IISER Kolkata Integrated PhD Student IISER Kolkata 2019  
7 55505 Mr. Manish Kumar Male IISER Kolkata Integrated Ph.D. IISER Kolkata 2021  
8 55603 Mr. Prabal Acharya Male Visvesvaraya National Institute of Technology PhD Research Scholar National Institute of Technology Rourkela 2020  
9 55829 Ms Evana Islam Sarkar Female IIT Bhubaneswar PhD Student Pondicherry University 2019  
10 55923 Mr. Debanjit Mondal Male IISER KOLKATA Integrated PhD IISER Kolkata 2022  
11 55977 Ms Dipika Robi Das Female Indian Institute of Technology Hyderabad PhD Visvesvaraya National Institute of Technology Nagpur 2022  
12 55983 Mr. Pankaj Roy Male Indian Institute of Technology Guwahati PhD Indian Institute of Technology Kanpur 2022  
13 56163 Mr. Anil Rathi Male Indian Institute of Technology Kanpur PhD Indian Institute of Technology Bombay 2020  
14 56173 Ms Saloni Gupta Female BANARAS HINDU UNIVERSITY RESEARCH SCHOLAR KURUKSHETRA UNIVERSITY 2019  
15 56210 Ms. Vijaya Dharshini T Female Bharathiar university -Sri G. V. G. Visalakshi college for women M. Sc Student Bharathiar university, Sri G. V. G. Visalakshi college for womenSri GVG Visalakshi college for women Appeared  
16 56286 Ms. Shreya Rajeshbhai Chauhan Female Institute of Infrastructure, Technology, Research And Management (IITRAM) PhD Student Sardar Patel University, Vallabh Vidyanagar, Gujarat 2020  
17 56295 Ms. Ankita Roy Chowdhury Female Indian Institute of Technology Hyderabad Ph.D. IIT (ISM), Dhanbad 2021  
18 56305 Mr Himanshu Shekhar Male Indian Institute of Science Education and Research, Vithura, Thiruvananthapuram, kerela MSc Student Indian Institute of Science Education and Research, Vithura, Thiruvananthapuram, kerela 2024  
19 56340 Mr. Arindam Basak Male Indian Institute of Technology Kharagpur PhD IIT Patna 2020  
20 56406 Ms. Rupali Sharma Female Indian Institute of Technology Kharagpur PhD Indian Institute of Technology Kharagpur 2022  
21 56407 Mr. Mohmedmunavvar Mubarak Bapu Male IIT Kanpur PhD Sardar Patel University 2018  
22 56423 Mr. Rishi Das Male IIT Bombay Ph.D. University of Calcutta 2021  
23 56455 Ms. Swati Garg Female Indian Institute of Technology Ropar PhD Panjab University Chandigarh 2018 18. Mar. 2024
24 56555 Ms Mousumi Mondal Female Indian Institute of Technology Guwahati PhD Visva-bharati University 2022 24. Jul. 2023
25 56562 Ms S Preethi . Female INDIAN INSTITUTE OF TECHNOLOGY HYDERABAD PhD Student NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL 2023  
26 56751 Mr. Surajit Pal Male IIT Bombay PhD IIT Kanpur 2022  
27 56762 Mr. Hari Om Jangid Male Indian Institute of Technology Kharagpur PhD IIT Kanpur, M.Sc. 2022  
28 56906 Mr. Subhodip Ghosh Male Iiser Thiruvananthapuram PhD Visva-Bharati 2021  
29 57093 Ms. Nayan Haldar Female IIT Guwahati PhD Diamond Harbour Womens' University 2020  
30 57387 Mr. Pashupati Nath Prasad Male Mahindra University PhD IIT Delhi 2021 17. Aug. 2023
Waiting list
1 56330 Mr. Shiba Biswas Male Indian Institute of Technology Kharagpur PhD Student University of North Bengal 2019  
2 55987 Mr. Susheel Kumar Male Banaras Hindu University Ph.D South Asian University New Delhi 2020  
3 56053 Ms. Sujata Sonkar Female Banaras Hindu University PhD University of Lucknow 2019  
4 57529 Ms Spoorthi K M Female MIT,manipal PH.D M.Sc 2023 18. Mar. 2024

 

How to Reach: 

TBA

School Short Name: 

maffm

Last Date Application: 

Monday, August 15, 2022

School Type: 

NCMW

Separate faculty form: 

0