Related papers: One-dimensional model equations for hyperbolic flu…

In this paper we study the equations governing the unsteady motion of an incompressible homogeneous generalized second grade fluid subject to periodic boundary conditions. We establish the existence of global-in-time strong solutions for…

The $\alpha$-patch model is used to study aspects of fluid equations. We show that solutions of this model form singularities in finite time and give a characterization of the solution profile at the singular time.

We study a nonlocal evolution equation that involves a pseudo-parabolic third-order term. The equation models almost uni-directional two-phase flow in Brinkman regimes. We prove the existence of weak solutions for this equation. We also…

This paper studies local existence and the singularity formation of the solutions of the one-dimensional hyperbolic Navier-Stokes equations, in particular proving the gradient blow-up of the derivatives of the solutions. The underlying…

We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the…

The flow of the relativistic imperfect fluid in two dimensions is discussed. We calculate the symmetry group of the energy-momentum tensor conservation equation in the ultrarelativistic limit. Group-invariant solutions for the…

Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But the usual Maxwell models allow one to define well motions…

In this work, we consider fluid-structure interaction simulation with nonlinear hyperelastic models in the solid part. We use a partitioned approach to deal with the coupled nonlinear fluid-structure interaction problems. We focus on…

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…

For ideal fluid flow with zero surface tension and gravity, it remains unknown whether local singularities on the free surface can develop in well-posed initial value problems with smooth initial data. This is so despite great advances over…

We find and classify self-similar solutions of the curve shortening flow in standard hyperbolic 2-space. Together with earlier work of Halld\'orsson on curve shortening flow in the plane and Santos dos Reis and Tenenblat in the 2-sphere,…

We investigate a holographic model of superfluid flows with an external repulsive potential. When the strength of the potential is sufficiently weak, we analytically construct two steady superfluid flow solutions. As the strength of the…

Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial…

In this paper, we investigate the formation of singularity for general two dimensional and radially symmetric solutions for rotating shallow water system from different aspects. First, the formation of singularity is proved via the study…

It was shown in [PRL 114, 138301 (2015)] that a remarkably simple dynamical model exhibits many of the complex flow regimes and non-equilibrium phase transitions characteristic of complex fluids. By removing extraneous detail, this simplest…

This paper is devoted to describe the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate the number of them, we also estimate…

This article concerns the formation of finite-time singularities in solutions to quasilinear hyperbolic systems with small initial data. By constructing a special test function, we first present a simpler proof of the main result in…

We revisit the general analytic solution space for relativistic $(1+1)$-dimensional hydrodynamics for a perfect fluid flowing along the longitudinal direction. We work out the explicit one-parameter family of interpolating flows between…

In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…

We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear…