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Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density $\rho$ which either falls off at infinity or has compact support. The solutions have finite mass, finite…

Analysis of PDEs · Mathematics 2017-09-26 Uwe Brauer , Lavi Karp

We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…

Analysis of PDEs · Mathematics 2017-10-02 Miroslav Bulíček , Josef Málek , Vít Průša , Endre Süli

In the first part of this work, we investigate the Cauchy problem for the $d$-dimensional incompressible Oldroyd-B model with dissipation in the stress tensor equation. By developing a weighted Chemin-Lerner framework combined with a…

Analysis of PDEs · Mathematics 2025-04-18 Tao Liang , Yongsheng Li , Xiaoping Zhai

We consider a system of partial differential equations describing the steady flow of a compressible heat conducting Newtonian fluid in a three-dimensional channel with inflow and outflow part. We show the existence of a strong solution…

Analysis of PDEs · Mathematics 2012-12-03 Tomasz Piasecki , Milan Pokorny

We investigate the existence of weak solutions to a certain system of partial differential equations, modelling the behaviour of a compressible non-Newtonian fluid for small Reynolds number. We construct the weak solutions despite the lack…

Analysis of PDEs · Mathematics 2023-05-24 Milan Pokorný , Maja Szlenk

We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is assumed to occupy a horizontally infinite…

Analysis of PDEs · Mathematics 2026-03-24 Jae Ho Choi , Ian Tice

In this paper we show that the rotational Smagorinsky model for turbulent flows, can be put, for a wide range of parameters in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions a)…

Analysis of PDEs · Mathematics 2021-07-02 Luigi C. Berselli , Alex Kaltenbach , Roger Lewandowski , Michael Růžička

This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…

Analysis of PDEs · Mathematics 2013-11-25 J. A. Carrillo , Y. -P. Choi , T. K. Karper

We consider a confined sheared active polar liquid crystal with a uniform orientation and study the effect of variations in the magnitude of polarization. Restricting our analysis to one-dimensional geometries, we demonstrate that with…

Soft Condensed Matter · Physics 2022-12-13 Aurore Loisy , Anthony P. Thompson , Jens Eggers , Tanniemola B. Liverpool

We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen--Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The…

Analysis of PDEs · Mathematics 2020-11-19 Hengrong Du , Changyou Wang

In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise…

Soft Condensed Matter · Physics 2017-07-06 Elisabeth Agoritsas , Kirsten Martens

Analytic expressions for the speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting steady, symmetric and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the…

Fluid Dynamics · Physics 2014-06-23 Abuzar A. Siddiqui , Akhlesh Lakhtakia

In this paper, we study the existence of solutions of stochastic incompressible non-Newtonian fluid models in $\mathbb{R}$. For the existence of solutions, we assume that the extra stress tensor $S$ is represented by $S({\mathbb A}) =…

Analysis of PDEs · Mathematics 2025-03-12 Tongkeun Chang , Minsuk Yang

In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type…

Analysis of PDEs · Mathematics 2021-03-03 Francesco De Anna , Joshua Kortum , Anja Schlömerkemper

We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…

Analysis of PDEs · Mathematics 2026-01-26 Anna Abbatiello , Miroslav Bulíček , Petr Kaplický

We introduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill the weak-strong uniqueness principle and the semi-flow property, and the set of solutions…

Analysis of PDEs · Mathematics 2022-11-23 Thomas Eiter , Robert Lasarzik

On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…

Soft Condensed Matter · Physics 2015-12-02 Ilya Peshkov , Miroslav Grmela , Evgeniy Romenski

This article is devoted to questions concerning the existence of solutions for partial differential equation problems modeling granular flows. The models studied take into account the complex threshold rheology of these flows, as well as…

Analysis of PDEs · Mathematics 2025-05-26 Laurent Chupin , Thierry Dubois

We study the problem of existence and uniqueness of strong solutions to a degenerate quasilinear parabolic non-Newtonian thin-film equation. Originating from a non-Newtonian Navier--Stokes system the equation is derived by lubrication…

Analysis of PDEs · Mathematics 2019-10-18 Christina Lienstromberg , Stefan Müller

Our purpose is to show the existence of weak solutions for unsteady flow of non-Newtonian incompressible nonhomogeneous, heat-conducting fluids with generalised form of the stress tensor without any restriction on its upper growth.…

Analysis of PDEs · Mathematics 2015-11-17 Bartłomiej Matejczyk , Aneta Wróblewska-Kamińska