New Perspectives in Mathematical Fluid Mechanics

This volume brings together lecture notes from the two most recent editions of the EMS Summer School Mathematical Aspects of Fluid Flows, held in Kacov, Czech Republic, in May 2019 and 2024. The lectures were taught by leading experts in various fields of mathematical fluid mechanics and offer the current state of the art and emerging trends in the field.

The book is organized into two parts:

Part I features lecture notes from the 2024 edition, covering quantum fluids, mathematical models of tumor growth, and fluid mixtures each explored from a mathematical perspective.

Part II includes two contributions from the 2019 edition, whose publication was delayed due to the Covid-19 pandemic. These chapters focus on the regularity theory of compressible and incompressible fluid flows, giving an interesting overview of the developments in the field.

This volume is an ideal resource for graduate students, early-career researchers, and specialists working in partial differential equations, fluid mechanics, and related areas.

Part I. Lectures from Kácov school 2024. - Chapter 1. An Introduction to the Mathematical Theory of Quantum Fluids. - Chapter 2. Singular Limits Arising in Mechanical Models of Tissue Growth. - Chapter 3. Mathematical Modeling of Fluids from the Kinetic Theory. - Part II. Lectures from Kácov school 2019. - Chapter 4. Lecture Notes on Intermittent Weak Solutions of the Three-dimensional Navier-Stokes Equations. - Chapter 5. Conserved Quantities and Regularity in Fluid Dynamics.