相关论文: Symmetries of Conservation Laws

We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…

The Whitham Broer Kaup (WBK) equations provide a fundamental framework for modeling shallow water wave dynamics, effectively capturing both nonlinear and dispersive effects. In this study, we construct a new class of analytical and…

We study numerically the standard one pressure model of two fluid flows with energy equations. This system is not solved in time derivative. It has been transformed into an equivalent system solved in time derivative. We show that the…

We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle…

We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations…

For hyperbolic systems of conservation laws in one space dimension with a mathematical entropy, we define the notion of entropy velocity. Then we give sufficient conditions for such a system to be covariant under the action of a group of…

The paper is concerned with the boundary controllability of entropy weak solutions to hyperbolic systems of conservation laws. We prove a general result on the asymptotic stabilization of a system near a constant state. On the other hand,…

We present a symmetry classification of the linearised Navier-Stokes equations for a two-dimensional unbounded linear shear flow of an incompressible fluid. The full set of symmetries is employed to systematically derive invariant ansatz…

We present a conservation formulation and a numerical algorithm for the reduced-gravity shallow-water equations on a beta plane, subjected to a constant wind forcing that leads to the formation of double-gyre circulation in a closed ocean…

A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…

We propose a general hydrodynamic framework for systems with spontaneously broken approximate symmetries. The second law of thermodynamics naturally results in relaxation in the hydrodynamic equations, and enables us to derive a universal…

This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator and a multiplicative noise. Our proof for uniqueness is based…

Using the concept of variational tricomplex endowed with a presymplectic structure, we formulate the general notion of symmetry. We show that each generalized symmetry of a gauge system gives rise to a sequence of conservation laws that are…

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such…

The aim of this paper is to study a one dimensional model system of equations for ionized gas dynamics at high temperature where the gas is a mixture of two kinds of monatomic gas. In addition to the mass density, pressure, temperature and…

In this paper we study a non strictly system of conservation law when viscosity is present and viscosity is zero, which is studied in [10]. We show the existence and uniqueness of the solution in the space of generalized functions of…

Using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations thereby establishing their…

Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…

A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second law of thermodynamics. This observation easily generalizes to…

We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the…