Mathematical Fluid Mechanics

N​ew SIG Mathematical Fluid Mechanics was approved by SPC at the meeting during Spring Festival 2023 on the 12th May 2023.

The proposed SIG

Objectives

The aim of the MFM SIG is to establish a scientific contact platform for academic researchers, scholars and application oriented people working in the area of mathematical modeling in fluid mechanics. The MFM SIG would like to provide theoretical background, skills and expertise in rigorous analysis of mathematical models and tools used in various fields of applied fluid mechanics.

Scientific/technical focus

1. Theoretical analysis of mathematical models in continuum mechanics
2. Qualitative and quantitative properties of differential equations
3. Numerical analysis for fluid mechanics
4. Problems in fluid-structure interaction with applications
5. Analysis of hydrodynamic models in social and natural sciences
6. Applications of mathematical models in industrial, environmental and biomedical flows

Motivation & Landscape

The research and development in fluid mechanics is one of the key factors driving the boom in associated business applications. Experimental techniques and numerical methods have helped to significantly advance and broaden the knowledge of various fluid mechanics based phenomena. However the dramatically increasing amount (and high-resolution) of experimental data and numerical results available, forces everyone to reconsider the investigation strategies and modeling approaches. There is a need to increase efficiency, robustness and reliability of mathematical models and methods in use. The problems of well-posedness of mathematical models, existence, uniqueness or stability of their solutions became a crucial factor in actual state of the art as well as future development of the mathematical modeling. Although mathematics is not in the core of ERCOFTAC activities, it is certainly an essential cornerstone in the foundations of all mathematical models and tools being used.

Outline plans

The MFM SIG is planning to organize regular conferences and summer schools, complemented by topical workshops in collaboration with other, more practically and application oriented SIGs:

• Conference – MFMin series – larger bi-annual meeting, with invited keynote speakers, contributed talks and short presentations. The first kick-off conference in this series was held in August 2022 in Prague, two next meetings are scheduled for 2024 and 2026. The location of the conference can differ depending on the actual interests and availability of facilities, organizers and local funding.
• Summer School – Prague-Sum series – already established bi-annual series of summer schools covering always a single chosen fluid mechanics related topic, from the point of view of physics, mathematical modeling, numerical simulations and practical applications. The next (Stochastics in Fluids) summer school in this series is scheduled for August 2023. These summer schools usually include several minicourses held by world renowned experts, being complemented by a one day workshop (not limited to the topic of the summer school) where also students are allowed and encouraged to present their work. The lecture notes are regularly published as a book in Springer/Birkhauser within the Advances in Mathematical Fluid Mechanics book series (AMFM)
• Topical Workshop – smaller (and possibly shorter) irregular event focusing on selected problems arising in the actual research projects, applications and cooperation of SIG members. First workshop on Problems in Biomedical Fluid Mechanics is scheduled for June 2023 being held at the Institute of Mathematics CAS.

Short description

The MFM SIG is established as a scientific contact platform for academic researchers, scholars and application oriented people working in the area of mathematical modeling in fluid mechanics. The MFM SIG provides theoretical background, skills and expertise in rigorous analysis of mathematical models and tools used in various fields of applied fluid mechanics.

Coordinators

The SIG should appoint two Coordinators, whose role is to initiate and manage the activities of the group. There should be one senior (Chair) and one junior (Deputy), and they must belong to organisations that are ERCOFTAC members.

1. Workshop: Biomedical flows: Mathematical modeling and simulations – June 12-16, 2023, Prague, Czech Republic. Organized by Šárka Nečasová and Tomáš Bodnár, Institute of Mathematics CAS.
2. Summer School and Conference on Stability and dynamics in fluid mechanics and kinetic theory - July 10-14, 2023, Imperial College London, UK. Organized by Jacob Bedrossian (UCLA), Michele Coti Zelati (Imperial College London). This is a summer school/workshop, aimed mostly at PhD students and postdocs. The topics are at the interface between fluid mechanics and kinetic theory. This event will host two mini courses, one in fluid mechanics (by T. Drivas, Stony Brook) and one in kinetic theory (by L. Saint-Raymond, IHES), complemented by seven seminars by experts in both fields.
3. Summer School: Stochastics in Fluids – August 21-25, 2023, Prague, Czech Republic. Organized by Tomáš Bodnár (CTU Prague), Giovanni Paolo Galdi (University of Pittsburgh), Šárka Nečasová (IM CAS Prague). Sixth event in the bi-annual Prague-Sum series of summer schools organized since 2011.
4. Conference and Spring School on Multiscale Problems in Science and Technology – March/April, 2024, Dubrovnik, Croatia. Organized by Maria Neuss-Radu University of Erlangen-Nürnberg, Germany. This event is the fourth in a series organized at the Centre for Advanced Academic Studies in Dubrovnik, dealing with topics like: reactive flows, diffusion and transport in complex media; biophysical and biochemical processes in cells, tissue and organs; micro-structures and macroscopic properties of materials; biotechnological and medical applications. It is dedicated to the memory of Andro Mikelic who gave outstanding contributions to the field and was one of the initiators of the series of Dubrovnik multiscale workshops and schools.
5. Summer school: EVEQ 2024, International Summer School on Evolution Equations – June 2024, organized by Ondřej Kreml, Václav Mácha, Martin Kalousek from Institute of Mathematics, CAS, Prague, Czech Republic. Regular event organized since 1984 with 4 year period.
6. Conference: Mathematical Fluid Mechanics in 2024 – August 26-30, 2024. Organized by Šárka Nečasová and Tomáš Bodnár, Institute of Mathematics CAS.
7. Summer School in the Prague-Sum series – August 25-29, 2025, Prague, Czech Republic. Organized by Tomáš Bodnár (CTU Prague), Giovanni Paolo Galdi (University of Pittsburgh), Šárka Nečasová (IM CAS Prague). Seventh event in the bi-annual Prague-Sum series of summer schools organized since 2011.