Titlebook: Mathematics of Open Fluid Systems; Eduard Feireisl,Antonin Novotný Book 2022 The Editor(s) (if applicable) and The Author(s), under exclus

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Long Time Behaviourstems. As we do not impose any restrictions on the size of the data, the model covers fluids in a turbulent regime. Unfortunately, however, the weak solutions are not (known to be) uniquely determined by the data; therefore, the standard dynamical systems approach based on the concept of solution se

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Statistical Solutions, Ergodic Hypothesis, and Turbulence precisely, we show the existence of a . statistical solution on any shift invariant compact subset of the trajectory space . that consists of entire solutions. In particular, each .-limit set generated by a global bounded solution (., ., .) will support a stationary statistical solution. Our princi

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Systems with Prescribed Boundary Temperaturehe possibility to control the time evolution of the total energy/entropy by means of the data. The resulting . bounds along with the pressure estimates are essential for the existence theory. We have considered general Dirichlet boundary conditions for the velocity field, with the associated mass fl

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Eduard Feireisl,Antonin Novotnýonal costs. Supporting software for the examples and exercises is available (but the text does not require the reader to use or understand these particular codes). The author has been active in optimization for over thirty years in algor978-1-4899-8119-6978-0-387-24149-4

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2523-3343 ish the weak-strong uniqueness principle.  Finally, Part III addresses questions of asymptotic compactness and global boundedness of trajectories and briefly considers the statistical theory of turbulence and the validity of the ergodic hypothesis.978-3-030-94792-7978-3-030-94793-4Series ISSN 2523-3343 Series E-ISSN 2523-3351

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Eduard Feireisl,Antonin Novotnýarity with the behaviour of iterative algorithms such as Newton’s methodfor nonlinear equations in one variable. Most of the currently popular methods for continuous nonlinear opti978-1-4419-4621-8978-0-387-78723-7Series ISSN 1931-6828 Series E-ISSN 1931-6836