Related papers: Low regularity conservation laws for the Benjamin-…
In this paper we consider the periodic Benjemin-Ono equation. We will establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [20]. As an intermediate step, we also obtain a…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…
This paper studies the derivation and well-posedness of a class of high - order water wave equations, the fifth - order Benjamin - Bona - Mahony (BBM) equation. Low - order models have limitations in describing strong nonlinear and high -…
In this paper, we first extend the explicit formula \cite{gerard2023explicit} for the classical Benjamin-Ono equation to each flow of the Benjamin-Ono hierarchy on line. We then use this representation to derive two main applications.…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
The analysis of non-local regularisations of scalar conservation laws is an active research program. Applications of such equations are found in the modelling of physical phenomena such as traffic flow. In this paper, we propose a novel…
We establish the convergence to the equilibrium for various linear collisional kinetic equations (including linearized Boltzmann and Landau equations) with physical local conservation laws in bounded domains with general Maxwell boundary…
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we…
We consider weak solutions of the inhomogeneous non-cutoff Boltzmann equation in a bounded domain with any of the usual physical boundary conditions: in-flow, bounce-back, specular-reflection and diffuse-reflection. When the mass, energy…
We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic…
We introduce several mechanisms to dissipate the energy in the Benjamin-Bona-Mahony (BBM) equation. We consider either a distributed (localized) feedback law, or a boundary feedback law. In each case, we prove the global wellposedness of…
Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…
This article deals with the regularity of the entropy solutions of scalar conservation laws with discontinuous flux. It is well-known [Adimurthi et al., Comm. Pure Appl. Math. 2011] that the entropy solution for such equation does not admit…
Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are…
It is well known, thanks to Lax-Wendroff theorem, that the local conservation of a numerical scheme for a conservative hyperbolic system is a simple and systematic way to guarantee that, if stable, a scheme will provide a sequence of…
Motivated by the work of P.L. Lions and J-C. Rochet [12], concerning multi-time Hamilton-Jacobi equations, we introduce the theory of multi-time systems of conservation laws. We show the existence and uniqueness of solution to the Cauchy…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
In this paper we study some properties of propagation of regularity of solutions of the dispersive generalized Benjamin-Ono (BO) equation. This model defines a family of dispersive equations, that can be seen as a dispersive interpolation…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived.…