Related papers: A numerical exploration of first-order relativisti…
In this paper, we are concerned with the local-in-time well-posedness of a fluid-kinetic model in which the BGK model with density dependent collision frequency is coupled with the inhomogeneous Navier-Stokes equation through drag forces.…
We introduce a special stochastic perturbation of the flow of diffuse matter as a curve in the group of diffeomorphisms of flat n-dimensional torus such that the perturbed system yields a solution of Burgers equation in the tangent space at…
Fluid configurations in three-dimensions, displaying a plausible decay of regularity in a finite time, are suitably built and examined. Vortex rings are the primary ingredients in this study. The full Navier-Stokes system is converted into…
This paper introduces a novel class of initial data for which the three-dimensional incompressible Navier--Stokes equations yield unique global-in-time solutions. Building on a logarithmically improved regularity criterion, we impose a…
The $3$-D primitive equations and incompressible Navier-Stokes equations with full hyper-viscosity and only horizontal hyper-viscosity are considered on the torus, i.e., the diffusion term $-\Delta$ is replaced by $-\Delta+…
The evolution of an electrically conducting imcompressible fluid with nonconstant density can be described by a set of equations combining the continuity, momentum and Maxwell's equations; altogether known as the inhomogeneous…
We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier-Stokes equations are solved using a finite-difference projection method coupled with a…
This paper is concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system describing the one-dimensional motion of a viscous…
The study of fluids has been a topic of intense research for several hundred years. Over the years, this has further increased due to improved computational facility, which makes it easy to numerically simulate the fluid dynamics, which was…
The Navier-Stokes-Korteweg (NSK) system is a classical diffuse interface model which is based on van der Waals theory of capillarity. Diffuse interface methods have gained much interest to model two-phase flow in porous media. However, for…
Inspired by recent results on the non-equilibrium dynamics of many-body quantum systems, we study the classical hard rod problem in one dimension with initial domain wall condition. Hard rods are an integrable system, in the sense that for…
We present the first demonstration of finite-time gradient blow-ups in Israel-Stewart (IS) theories with 1+1D plane symmetry, mathematically showing the existence of smooth initial data that can evolve into shocks across three regimes: pure…
Navier-Stokes equations establish the hydrodynamical problem by definition. The importance of these equations is quite natural to understand if we focus on the role they assume in a large spectrum of dynamical problems which involve…
In recent years the equations of relativistic first-order viscous hydrodynamics, that is, the relativistic version of Navier-Stokes, have been shown to be well posed and causal under appropriate field redefinitions, also known as…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
Kinetic approaches are routinely employed to simulate the dynamics of systems that are too rarified to be described by the Navier-Stokes equations. However, generally they are far too computationally expensive to be applied for systems that…
In a previous work, we presented a class of initial data to the three dimensional, periodic, incompressible Navier-Stokes equations, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large.…
We consider a system of many hard rods moving in one dimension. As it is an integrable system, it possesses an extensive number of conserved quantities and its evolution on macroscopic scale can be described by generalised hydrodynamics.…
It is shown here that a subset of the implicit analytical shock solutions discovered by Becker and by Johnson can be inverted, yielding several exact closed-form solutions of the one-dimensional compressible Navier-Stokes equations for an…