Fluids Under Control The 2021 Prague-Sum Workshop Lectures

This volume presents state-of-the-art developments in theoretical and applied fluid mechanics. Chapters are based on lectures given at a workshop in the summer school Fluids under Control, held in Prague on August 25, 2021. Readers will find a thorough analysis of current research topics, presented by leading experts in their respective fields. Specific topics covered include:

• Magnetohydrodynamic systems
• The steady Navier-Stokes-Fourier system
• Boussinesq equations
• Fluid-structure-acoustic interactions

Fluids under Control will be a valuable resource for students interested in mathematical fluid mechanics.

On the weak and variational entropy solutions for the steady Navier-Stokes-Fourier system with Dirichlet boundary condition for the temperature.- Stability estimates for a viscous incompressible flow past a rigid body with time-dependent motion.- Existence and regularity of a magnetohydrodynamic system with Navier-type boundary conditions in 2-D.- On asymptotic stability of Boussinesq equations.- Controllability of one dimensional Burgers-particle interaction model.- Optimal control for two-dimensional Navier-Stokes equations with slippage.- Asymptotic behavior of the Navier-Stokes type problem.- On an approach to the global well-posedness of quasilinear parabolic- hyperbolic coupled system in unbounded domains.

Tomáš Bodnár is Associate Professor in the Department of Technical Mathematics Faculty of Mechanical Engineering at the Czech Technical University in Prague, as well as a researcher at the Institute of Mathematics, Czech Academy of Sciences. Research interests include numerical analysis, computational fluid mechanics, environmental and biological flows.