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Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The Large Eddy Simulations (LES) models are efficient tools to approximate turbulent fluids and an important step in the…

Analysis of PDEs · Mathematics 2018-05-23 Luigi C. Berselli , Stefano Spirito

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

Analysis of PDEs · Mathematics 2015-06-01 Sergio Frigeri

In this paper we consider the Zakharov system with periodic boundary conditions in dimension one. In the first part of the paper, it is shown that for fixed initial data in a Sobolev space, the difference of the nonlinear and the linear…

Analysis of PDEs · Mathematics 2012-02-24 Burak Erdogan , Nikolaos Tzirakis

We prove the existence of global-in-time weak solutions to a general class of models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains…

Analysis of PDEs · Mathematics 2015-07-21 John W. Barrett , Endre Süli

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity, have non-vanishing swirl and scatter…

Analysis of PDEs · Mathematics 2022-10-10 Yan Guo , Benoit Pausader , Klaus Widmayer

We consider the incompressible Navier-Stokes equations with spatially periodic boundary conditions. If the Reynolds number is small enough we provide an elementary short proof of the existence of global in time H\"older continuous…

Analysis of PDEs · Mathematics 2010-04-08 Gautam Iyer

We consider evolution (non-stationary) space-periodic solutions to the $n$-dimensional non-linear Navier-Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed…

Analysis of PDEs · Mathematics 2024-02-09 Sergey E. Mikhailov

We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a…

Analysis of PDEs · Mathematics 2020-07-15 A. Kh. Khanmamedov

In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations with degenerate viscosities is considered. By introducing some new variables and making use of the "quasi-symmetric…

Analysis of PDEs · Mathematics 2019-04-09 Zhouping Xin , Shengguo Zhu

For the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature, we obtain global…

Analysis of PDEs · Mathematics 2024-06-19 Yuebo Cao , Yi Peng , Ying Sun

This paper is concerned with pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a…

Dynamical Systems · Mathematics 2019-01-23 Xin-Guang Yang , Baowei Feng , Shubin Wang , To Fu Ma , Yongjin Lu

We investigate a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn-Hilliard equation for the…

Analysis of PDEs · Mathematics 2023-07-28 Andrea Di Primio , Maurizio Grasselli , Hao Wu

We consider a flow of non-Newtonian heat conducting incompressible fluid in a bounded domain subjected to the homogeneous Dirichlet boundary condition for the velocity field and the spatially inhomogeneous Dirichlet boundary condition for…

Analysis of PDEs · Mathematics 2022-10-12 Anna Abbatiello , Miroslav Bulíček , Petr Kaplický

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient…

Analysis of PDEs · Mathematics 2015-05-14 Maurizio Grasselli , Giulio Schimperna , Sergey Zelik

We examine a viscous Cahn-Hilliard phase-separation model with memory and where the chemical potential possesses a nonlocal fractional Laplacian operator. The existence of global weak solutions is proven using a Galerkin approximation…

Analysis of PDEs · Mathematics 2018-05-01 Eylem Öztürk , Joseph L. Shomberg

We find a global a priori estimate for solutions to the Navier-Stokes equations with periodic boundary conditions guaranteeing in view of the Serrin type condition the existence of global regular solutions. We derive the following estimate…

Analysis of PDEs · Mathematics 2019-07-23 Wojciech M. Zajaczkowski

In this paper, we consider the Cauchy problem for the three-dimensional barotropic compressible Navier-Stokes equations with density-dependent viscosities. By considering the system as an elliptic-dominated structure and defining suitable…

Analysis of PDEs · Mathematics 2024-08-09 Xiangdi Huang , Jiaxu Li , Rong Zhang

This article is devoted to the study of multivalued semigroups and their asymptotic behavior, with particular attention to iterations of set-valued mappings. After developing a general abstract framework, we present an application to a time…

Numerical Analysis · Mathematics 2012-02-09 Michele Coti Zelati , Florentina Tone

In this paper we propose some Harris-like criteria in order to study the long time behavior of general positive and periodic semiflows. These criteria allow us to obtain new existence results of principal eigenelements, and their…

Analysis of PDEs · Mathematics 2024-11-05 Adil El Abdouni

We establish the global existence of a class of weak solutions to the isentropic compressible Navier-Stokes equations in a half-plane with Dirichlet boundary conditions, allowing for vacuum both in the interior and at infinity, under a…

Analysis of PDEs · Mathematics 2026-02-05 Shuai Wang , Xin Zhong