Stochastically Forced Compressible Fluid Flows
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| Author | : Dominic Breit |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 344 |
| Release | : 2018-01-22 |
| Genre | : Mathematics |
| ISBN | : 3110492555 |
This book contains a first systematic study of compressible fluid flows subject to stochastic forcing. The bulk is the existence of dissipative martingale solutions to the stochastic compressible Navier-Stokes equations. These solutions are weak in the probabilistic sense as well as in the analytical sense. Moreover, the evolution of the energy can be controlled in terms of the initial energy. We analyze the behavior of solutions in short-time (where unique smooth solutions exists) as well as in the long term (existence of stationary solutions). Finally, we investigate the asymptotics with respect to several parameters of the model based on the energy inequality. Contents Part I: Preliminary results Elements of functional analysis Elements of stochastic analysis Part II: Existence theory Modeling fluid motion subject to random effects Global existence Local well-posedness Relative energy inequality and weak–strong uniqueness Part III: Applications Stationary solutions Singular limits
| Author | : Miroslav Bulíček |
| Publisher | : Springer |
| Total Pages | : 190 |
| Release | : 2018-09-26 |
| Genre | : Mathematics |
| ISBN | : 331994343X |
The book presents recent results and new trends in the theory of fluid mechanics. Each of the four chapters focuses on a different problem in fluid flow accompanied by an overview of available older results. The chapters are extended lecture notes from the ESSAM school "Mathematical Aspects of Fluid Flows" held in Kácov (Czech Republic) in May/June 2017. The lectures were presented by Dominic Breit (Heriot-Watt University Edinburgh), Yann Brenier (École Polytechnique, Palaiseau), Pierre-Emmanuel Jabin (University of Maryland) and Christian Rohde (Universität Stuttgart), and cover various aspects of mathematical fluid mechanics – from Euler equations, compressible Navier-Stokes equations and stochastic equations in fluid mechanics to equations describing two-phase flow; from the modeling and mathematical analysis of equations to numerical methods. Although the chapters feature relatively recent results, they are presented in a form accessible to PhD students in the field of mathematical fluid mechanics.
| Author | : Franco Flandoli |
| Publisher | : Springer Nature |
| Total Pages | : 206 |
| Release | : 2023-06-11 |
| Genre | : Mathematics |
| ISBN | : 9819903858 |
This book is devoted to stochastic Navier–Stokes equations and more generally to stochasticity in fluid mechanics. The two opening chapters describe basic material about the existence and uniqueness of solutions: first in the case of additive noise treated pathwise and then in the case of state-dependent noise. The main mathematical techniques of these two chapters are known and given in detail for using the book as a reference for advanced courses. By contrast, the third and fourth chapters describe new material that has been developed in very recent years or in works now in preparation. The new material deals with transport-type noise, its origin, and its consequences on dissipation and well-posedness properties. Finally, the last chapter is devoted to the physical intuition behind the stochastic modeling presented in the book, giving great attention to the question of the origin of noise in connection with small-scale turbulence, its mathematical form, and its consequences on large-scale properties of a fluid.
| Author | : Roland Glowinski |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 232 |
| Release | : 2022-09-19 |
| Genre | : Mathematics |
| ISBN | : 3110785013 |
This text on finite element-based computational methods for solving incompressible viscous fluid flow problems shows readers how to split complicated computational fluid dynamics problems into a sequence of simpler sub-problems. A methodology for solving more advanced applications such as hemispherical cavity flow, cavity flow of an Oldroyd-B viscoelastic flow, and particle interaction in an Oldroyd-B type viscoelastic fluid is also presented.
| Author | : Carlos Parés |
| Publisher | : Springer Nature |
| Total Pages | : 376 |
| Release | : |
| Genre | : |
| ISBN | : 3031552601 |
| Author | : Habib Ammari |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 122 |
| Release | : 2023-11-06 |
| Genre | : Mathematics |
| ISBN | : 3110784963 |
Metamaterials are advanced composite materials which have exotic and powerful properties. Their complicated microstructures make metamaterials challenging to model, requiring the use of sophisticated mathematical techniques. This book uses a from-first-principles approach (based on boundary integral methods and asymptotic analysis) to study a class of high-contrast metamaterials. These mathematical techniques are applied to the problem of designing graded metamaterials that replicate the function of the cochlea.
| Author | : Alexander V. Bobylev |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 212 |
| Release | : 2024-09-23 |
| Genre | : Mathematics |
| ISBN | : 3110551004 |
This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.
| Author | : Zhi-Zhong Sun |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 432 |
| Release | : 2023-05-08 |
| Genre | : Mathematics |
| ISBN | : 3110796015 |
Introduces recent research results of finite difference methods including important nonlinear evolution equations in applied science. The presented difference schemes include nonlinear difference schemes and linearized difference schemes. Features widely used nonlinear evolution equations such as Burgers equation, regular long wave equation, Schrodinger equation and more. Each PDE model includes details on efficiency, stability, and convergence.
| Author | : Bruno Després |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 174 |
| Release | : 2022-08-22 |
| Genre | : Mathematics |
| ISBN | : 3110783185 |
This book uses numerical analysis as the main tool to investigate methods in machine learning and A.I. The efficiency of neural network representation on for polynomial functions is studied in detail, together with an original description of the Latin hypercube method. In addition, unique features include the use of Tensorflow for implementation on session and the application n to the construction of new optimized numerical schemes.
| Author | : Claude Le Bris |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 158 |
| Release | : 2019-06-17 |
| Genre | : Mathematics |
| ISBN | : 311063550X |
This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.
