Related papers: Commuting Flows and Conservation Laws for Noncommu…
Scalar conservation laws with non-convex fluxes have shock wave solutions that violate the Lax entropy condition. In this paper, such solutions are selected by showing that some of them have corresponding traveling waves for the equation…
We derive a class of energy preserving boundary conditions for incompressible Newtonian flows and prove local-in-time well-posedness of the resulting initial boundary value problems, i.e. the Navier-Stokes equations complemented by one of…
Using our previous results on the systematic construction of invariant differential operators for non-compact semisimple Lie groups we classify the conservation laws in the case of SO(p,q).
This study derives conservative and skew-symmetric formulations of the incompressible flow equations in a terrain-following sigma-coordinate system that preserve key structural properties of the Cartesian formulation. Unlike conventional…
In the Second Order Theories (SOT) of real relativistic fluids, the non-ideal properties of the flows are described by a new set of dynamical tensor variables. In this work we explore the non-linear dynamics of those variables in a…
For a class of generalized integrable hierarchies associated with affine (twisted or untwisted) Kac-Moody algebras, an explicit representation of their local conserved densities by means of a single scalar tau-function is deduced. This…
The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to…
In the case of scalar conservation laws $$ u_{t} + f(u)_{x}~=~0,\qquad t\geq 0, x\in\mathbb{R}, $$ with uniformly strictly convex flux $f$, quantitative compactness estimates - in terms of Kolmogorov entropy in ${\bf L}^{1}_{loc}$ - were…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…
We propose a mathematical framework to the study of scalar conservation laws with moving interfaces. This framework is developed on a LWR model with constraint on the flux along these moving interfaces. Existence is proved by means of a…
A conservation-consistent boundary condition is proposed for nonlinear models of soluble-surfactant-laden falling films, ensuring exact conservation of total surfactant mass. The formulation resolves an inconsistency in widely used reduced…
We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a~kinetic formulation…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
In this paper, we construct the additional flows of the noncommutative Kadomtsev-Petviashvili(KP) hierarchy and the additional symmetry flows constitute an infinite dimensional Lie algebra $W_{1+\infty}$. In addition, the generating…
In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities coupled via surface conservation laws of excess surface quantities. While this approach is for microscopically sharp interfaces, its applicability…
This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to full discrete conservation of…
We present the noncanonical Hamiltonian structure of the relativistic Euler equations for a perfect fluid in Minkowski spacetime. By identifying the system's noncanonical Poisson bracket and Hamiltonian, we show that relativistic fluid…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…