Related papers: Potential Conservation Laws
We present the full thermodynamics of a fluid confined by an arbitrary external potential based on the virial expansion of the grand potential. The fluid may be classical or quantum and it is assumed that interatomic interactions are…
We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be utilized to solve the model. We show that for models where the conservation laws can be written in one-sided forms, like…
It is known that in low dimensions WDVV equations can be rewritten as commuting quasilinear bi-Hamiltonian systems. We extend some of these results to arbitrary dimension $N$ and arbitrary scalar product $\eta$. In particular, we show that…
This article is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical…
In this note a new way to construct the characteristics of conservations laws of integrable chiral-type systems is proposed.
In this paper, we present infinitely many conserved densities satisfying particular conservation law $F_{t}=(2uF)_{x}$ for the generalized Riemann equations at $N=2,3,4$. In the $N=2$ case, we also construct conserved densities…
This paper develops some mathematical models arising in behavioral sciences, particularly in psychology, which are formalized via general preferences with variable ordering structures. Our considerations are based on the recent variational…
The main goal of the paper is to define and use a condition sufficient to choose a unique solution to conservation law systems with a singular measure in initial data. Different approximations can lead to solutions with different…
This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…
We present a general theory of potentials that support bound states at positive energies (bound states in the continuum). On the theoretical side, we prove that, for systems described by nonlocal potentials of the form $V(r,r')$, bound…
We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways.…
In this paper we extend results obtained in [3] and [5]. By considering a semi linear conservation law with velocity in $L^\infty$, we prove by fixed point arguments existence and uniqueness result and even in a penalized situation.
A theorem due to Nail H. Ibragimov (2007) provides a connection between symmetries and conservation laws for arbitrary differential equations. The theorem is valid for any system of differential equations provided that the number of…
In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…
The interrelationship between energy and probability conservation is explored from the point of view of statistical physics and non-relativistic quantum mechanics. The simultaneous validity of the law of conservation of energy and the…
An extension is proposed to the internal symmetry transformations associated with mass, entropy and other Clebsch-related conservation in geophysical fluid dynamics. Those symmetry transformations were previously parameterized with an…
Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish,…
One dimensional systems sometimes show pathologically slow decay of currents. This robustness can be traced to the fact that an integrable model is nearby in parameter space. In integrable models some part of the current can be conserved,…
This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87…
Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and…