Compressible non-Newtonian Fluid Research Articles

Bounded absorbing sets for compressible non-Newtonian fluids

Bounded absorbing sets for compressible non-Newtonian fluids

Remark on the Local Well-Posedness of Compressible Non-Newtonian Fluids with Initial Vacuum

We discuss in this short note the local-in-time strong well-posedness of the compressible Navier–Stokes system for non-Newtonian fluids on the three dimensional torus. We show that the result established recently by Kalousek, Mácha, and Nečasova in https://doi.org/10.1007/s00208-021-02301-8 can be extended to the case where vanishing density is allowed initially. Our proof builds on the framework developed by Cho, Choe, and Kim in https://doi.org/10.1016/j.matpur.2003.11.004 for compressible Navier–Stokes equations in the case of Newtonian fluids. To adapt their method, special attention is given to the elliptic regularity of a challenging nonlinear elliptic system. We show particular results in this direction, however, the main result of this paper is proven in the general case when elliptic W2,p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$W^{2,p}$$\\end{document}-regularity is imposed as an assumption. Also, we give a finite time blow-up criterion.

On the Global Existence for a Class of Compressible Non-Newtonian Fluids with Inhomogeneous Boundary Data

On the Global Existence for a Class of Compressible Non-Newtonian Fluids with Inhomogeneous Boundary Data

Time decay of solutions for compressible isentropic non-Newtonian fluids

In this paper, we consider the Cauchy problem of a compressible Navier–Stokes system of Eills-type non-Newtonian fluids. We investigate the time decay properties of classical solutions for the compressible non-Newtonian fluid equations. More specifically, we construct a new linearized system in terms of a combination of the solutions, and then we investigate the long-time behavior of the Cauchy problem for the three-dimensional isentropic compressible Eills-type non-Newtonian fluids with an initial perturbation.

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

Global existence and time behaviour of strong solution to a compressible non-Newtonian fluid

This paper studies the initial–boundary problem of a one-dimensional compressible non-Newtonian fluid with vacuum, whose power-law exponent is r∈(1,2). The global existence of strong solution is obtained by combining the local existence and a priori estimates, provided that H1-norm of the initial density is small enough and the initial data satisfies a compatibility condition. Moreover, the time behaviour of ‖ρut‖L2 and ‖ux‖Lr are obtained on time interval of existence. As a byproduct, a blow-up criterion in term of ‖uxx‖L2 for strong solution to the initial–boundary value problem of the compressible non-Newtonian fluid. Our result is an extension of the work of Yuan and Xu (2008), where the local strong solution in one-dimensional space is obtained. Our analysis is based on some new mathematical techniques.

Global Existence of Strong Solutions to the Cauchy Problem for a One-Dimensional Compressible Non-Newtonian Fluid

Global Existence of Strong Solutions to the Cauchy Problem for a One-Dimensional Compressible Non-Newtonian Fluid

The existence and limit behavior of the shock layer for 1D stationary compressible non-Newtonian fluids

The existence and limit behavior of the shock layer for 1D stationary compressible non-Newtonian fluids

Well-posedness for a class of compressible non-Newtonian fluids equations

The purpose of this paper is to deal with the issue of well-posedness for a class of non-Newtonian fluid dynamics equations. The equations describing the motion of such fluids are characterized by a non-linear constitutive law relating the state of stress to the rate of deformation. We show the local-in-time existence and uniqueness of strong solutions to two important models: the Power Law model and the Bingham model. While our result for the first model holds over a periodic domain Ω=R3, the result obtained on the second model is limited to the one-dimensional case. This is because Bingham's constitutive law is discontinuous due to phase transition that may appear during the time when flows change nature, particularly from liquid motion to rigid motion and vice-versa. This property reduces the probability of showing smooth solutions to such a system in higher dimension space.

Stationary solutions to a compressible non-Newtonian fluid with general boundary conditions

This paper is concerned with the steady-state equations describing a motion of some non-Newtonian fluids whose viscosity has a power-structure with an exponent r. The existence of weak solutions is established through a two-level approximation procedure and weak convergence argument whenever r > 2, which is the optimal bound for the existence of weak solutions.

Existence and uniqueness of strong solutions for a class of compressible non-Newtonian fluids with singularity

Existence and uniqueness of strong solutions for a class of compressible non-Newtonian fluids with singularity

A WCSPH two-phase mixture model for tsunami waves generated by granular landslides

An advanced weakly compressible smooth particle hydrodynamics (WCSPH) two-phase mixture model is developed in this study to simulate the motion of granular landslides as well as their resulting tsunami waves. The governing equations of fluid and granular phases are established based on the two-phase mixture theory. The granular phase is assumed to be a weakly compressible non-Newtonian fluid, and the regularized visco-inertial rheology model is adopted to calculate its effective viscosity. The water phase is considered as a weakly compressible Newtonian fluid, and the large eddy simulation (LES) turbulence model is adopted to describe the turbulence effect of the fluid. The interphase force controls the momentum exchange between fluid and granular phases. The artificial diffusion term and particle shifting technique are adopted to improve the accuracy and stability of numerical calculation. This developed numerical model was applied to simulate submarine and subaerial granular landslide-tsunamis, and the results were compared with corresponding experimental data. The results show that the current model can adequately represent the generation and propagation of tsunami waves and the motion and deformation of granular landslides. Compared with the traditional two-phase granular flow models, the current model has higher accuracy and wider application scenarios.

Global weak solutions to a three-dimensional compressible non-Newtonian fluid

Global weak solutions to a three-dimensional compressible non-Newtonian fluid

Local-in-time existence of strong solutions to a class of the compressible non-Newtonian Navier–Stokes equations

The aim of this article is to show a local-in-time existence of a strong solution to the generalized compressible Navier-Stokes equations for arbitrarily large initial data. The goal is reached by \(L^p\)-theory for linearized equations which are obtained with help of the Weis multiplier theorem and can be seen as a generalization of the work of Enomoto and Shibata (Funkcial Ekvac 56(3):441–505, 2013) (devoted to compressible fluids) to compressible non-Newtonian fluids.

Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum

In this article, we investigate an initial and boundary value problem for a class of compressible non-Newtonian fluids, provided the initial energy is small and the initial density containing the vacuum state is allowed. For p>2, we obtain the existence and uniqueness of the global strong solution for this problem in a one-dimensional bounded interval.

Stability and dynamics for a nonlinear one-dimensional full compressible non-Newtonian fluids

In this paper, we concern with the existence of global attractors for a one-dimensional full compressible non-Newtonian fluid model defined on bounded domain. Using some delicate regular estimates and energy functional to obtain the continuity of semigroup and dissipation respectively, the long time behavior of global solution has been investigated, which is a further of [ 31 ].

一维空间中可压缩变指数增长非牛顿流体模型的强解

一维空间中可压缩变指数增长非牛顿流体模型的强解

Global strong solutions of a class of non-Newtonian fluids with small initial energy

In this paper, we are concerned with an initial–boundary value problem for a class of non-Newtonian fluids. The viscosity term of momentum equation possesses singularity and nonlinearity, and the initial vacuum is allowed. The main feature which distinguishes this paper from other related works lies in the fact that we study the global strong solution of the compressible non-Newtonian fluids with singularity and vacuum in one-dimensional bounded intervals, and show that there exists a unique global-in-time strong solution to the problem while the initial energy is small.

带有Power-Law型粘性项的可压缩非牛顿流的光滑解

带有Power-Law型粘性项的可压缩非牛顿流的光滑解

Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids

In this paper, we study the large time behaviors of boundary layer solution of the inflow problem on the half space for a class of isentropic compressible non-Newtonian fluids. We establish the existence and uniqueness of the boundary layer solution to the non-Newtonian fluids. Especially, it is shown that such a boundary layer solution have a maximal interval of existence. Then we prove that if the strength of the boundary layer solution and the initial perturbation are suitably small, the unique global solution in time to the non-Newtonian fluids exists and asymptotically tends toward the boundary layer solution. The proof is given by the elementary energy method.