The problems of related to rotation and fluids can be found in many areas of applications. Their mathematical modeling, experimental investigation and numerical simulations are often using specific methods and tools. The aim of this summer school is to present a comprehensive series of lectures on various aspects of rotation and fluids and their role in mathematical analysis and numerical simulation of different types of flows. The summer school is organized as a multidisciplinary event with topics ranging from theoretical and numerical mathematics up to physics and applications. The emphasize will be on models related to topics originating in environmental, biomedical and industrial applications. The summer course is prepared for graduate students, young scientists, and other interested specialists. Besides of the course lectures, the program will include a one day workshop (on Wednesday, August 27, 2025) dedicated to short, more advanced lectures given by attending scientists.

Organized by:

• Tomáš Bodnár – Czech Technical University in Prague, ERCOFTAC PC Czech Republic
• Giovanni Paolo Galdi – University of Pittsburgh, USA
• Šárka Nečasová – Institute of Mathematics, Czech Academy of Sciences

Web: http://prague-sum.com/

Main Topics:

• Rotating bodies in fluids
• Vortices and rotation in environmental flows
• Rotating machines – pumps, turbines
• Rotating wings – propellers, hellicopters
• Astronomical flows
• Vortex methods for CFD
• Vorticity & rotation in turbulence

Summer School courses:

• Compact minicourses (typically 4 lectures by 50 minutes each) will be presented by the invited speakers (up to 28 lectures in total)
• The lectures will be scheduled in larger blocks within four full days (Monday August 25, Tuesday 26, Thursday 28, Friday 29).

Workshop presentations:

• Workshop is organized on Wednesday, August 27, 2025.
• Shorter talks (up to 30 minutes), given by invited or contributing speakers
• Talks will be selected from the proposed contributions based on their quality and suitability with respect to the main topic of the summer course.
• Remaining presentation, including those of the students of the summer school, will be presented in the form of posters.
• All the young researchers profiting from the ERCOFTAC support will be obliged to presenttheir own work (poster or talk) during the Workshop day.

Relation to ERCOFTAC:

• The participants coming from ERCOFTAC member institutions are eligible for substantial (20%) discount from all registration fees.
  This will be advertised on the Summer School web page.

History of the event

The above presented Summer School is already seventh in the series started in 2011. The previous events were:

• Fluid-Structure Interaction for Biomedical Applications: August 29 - September 2, 2011
• Non-Homogeneous Fluids and Flows: August 27 - August 31, 2012
• Particles in Flows: August 25 - August 31, 2014
• Fluids under Pressure: August 29 - September 2, 2016
• Waves in Flows: August 27 - August 31, 2018
• Fluids Under Control: August 23 – 27, 2021
• Stochastics in Fluids: August 21 – 25, 2023

Now it has developed into a regular (bi-annual) series of thematic summer schools running under a common label “Prague-Sum”. All the information, presentations, course materials as well as the photos from those events are made openly available to public at the dedicated permanent web page https://prague-sum.com/

The events in 2011, 2014, 2016, 2018, 2021 and 2023 were supported by ERCOFTAC and used its logo. The summer schools are organized as purely non-profit events. All the money gained from the registration fees and various grants are exclusively (and completely) spent to organization costs (including also refreshment, lunches, social programme, etc.), reimbursement of the travel and living costs for invited speakers and young researchers.

During the years, the summer school gained quite a good reputation and excellent feedback from the participants. Based on the outstanding quality of the speakers and courses, five books were already published by Birkhäuser – Springer (two more books, based on Stochastics in Fluids from 2023, are under preparation). The already published books are:

1. Fluid-Structure Interaction and Biomedical Applications (based on the summer school from 2011) https://link.springer.com/book/10.1007/978-3-0348-0822-4
2. Particles in Flows (based on the summer school from 2014) https://link.springer.com/book/10.1007/978-3-319-60282-0
3. Fluids Under Pressure (based on the summer school from 2016) https://link.springer.com/book/10.1007/978-3-030-39639-8
4. Waves in Flows (based on the summer school from 2018) https://link.springer.com/book/10.1007/978-3-030-67845-6
5. Waves in Flows - The 2018 Prague-Sum Workshop Lectures https://link.springer.com/book/10.1007/978-3-030-68144-9
6. Fluids Under Control (based on the summer school from 2021) https://link.springer.com/book/10.1007/978-3-031-47355-5
7. Fluids Under Control - The 2021 Prague-Sum Workshop Lectures https://link.springer.com/book/10.1007/978-3-031-27625-5