This volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods. Chapters are based on the lectures given at a workshop in the summer school Waves in Flows, held in Prague from August 27-31, 2018. A broad overview of cutting edge research is presented, with a focus on mathematical modeling and numerical simulations. Readers will find a thorough analysis of numerous state-of-the-art developments presented by leading experts in their respective fields. Specific topics covered include:

ChemorepulsionCompressible Navier-Stokes systemsNewtonian fluidsFluid-structure interactions

Waves in Flows: The 2018 Prague-Sum Workshop Lectures will appeal to post-doctoral students and scientists whose work involves fluid mechanics.

Semigroup theory for the Stokes operator with Navier boundary condition onLp spaces.- Theoretical and numerical results for a chemo-repulsion model with non-constant diffusion coefficients.- Remarks on the energy equality for the 3D Navier-Stokes equations.- Existence, uniqueness and asymptotic behavior of regular time-periodic viscous flow around a moving body.- Compressible Navier-Stokes system on a moving domain in theLp -Lq framework.- Some new properties of a suitable weak solution to the Navier-Stokes equations.- Existence, uniqueness and regularity for the second-gradient Navier-Stokes equations in exterior domains.- A review on rigorous derivation of reduced models for fluid - structure interaction systems.- Stability of a steady flow of an incompressible Newtonian fluid in an exterior domain.