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Non-Newtonian Compressible Fluids with Stochastic Right-Hand Side

  • 2025
  • OriginalPaper
  • Chapter
Published in:
Authors
Pavel Ludvík
Václav Mácha
Published in
Stochastics in Fluids
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the complex world of compressible non-Newtonian fluids, focusing on their mathematical description and the introduction of stochastic forces. The article begins by discussing the physical phenomena captured by these fluids, such as die swell and shear thinning/thickening. It then explores the mathematical challenges in proving the existence of weak solutions, highlighting the work of various researchers in this field. The main contribution of this article is the introduction of a novel concept of measure-valued solutions for nonlinear compressible Navier-Stokes equations with stochastic forces. The article provides a detailed proof of the existence of these solutions, using advanced mathematical tools such as Young measures and the Jakubowski-Skorokhod theorem. The article also discusses the implications of these findings for the study of non-Newtonian fluids and stochastic processes. The chapter concludes with a discussion of the potential applications of these findings in various industries, including engineering and physics.
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previous chapter Comparative Study of 2D-2D FEM-FSI and 2D-1D Reduced FD Models for Respiratory Flow Simulation
next chapter Weak-Strong Uniqueness for a Compressible Fluid-Rigid Body Interaction Problem with General Inflow-Outflow Boundary Data
Title
Non-Newtonian Compressible Fluids with Stochastic Right-Hand Side
Authors
Pavel Ludvík
Václav Mácha
Copyright Year
2025
Book
Stochastics in Fluids

Print ISBN: 978-3-032-02298-1

Electronic ISBN: 978-3-032-02299-8

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-032-02299-8_3
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