相关论文: A non-monotone conservation law for dune morphodyn…

Conservation laws are the pillars of physics. It's what we held on to when our imagination was challenged during the days of relativity or quantum mechanics. Their violation leads to the most absurd models, so excellently exercised in the…

Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations. Using group classification and Noether's theorem,…

We consider the inhomogeneous incompressible Euler equations including their local energy inequality as a differential inclusion. Providing a corresponding convex integration theorem and constructing subsolutions, we show the existence of…

We investigate a class of nonlocal conservation laws with the nonlinear advection coupling both local and nonlocal mechanism, which arises in several applications such as the collective motion of cells and traffic flows. It is proved that…

In this paper, approximate nonlinear self-adjointness for perturbed PDEs is introduced and its properties are studied. Consequently, approximate conservation laws which cannot be obtained by the approximate Noether theorem are constructed…

We investigate the hydrodynamic behavior and local equilibrium of the multilane exclusion process, whose invariant measures were studied in our previous paper \cite{mlt1a}. The dynamics on each lane follows a hyperbolic time scaling,…

We investigate real solutions of a C-integrable non-evolutionary partial differential equation in the form of a scalar conservation law where the flux density depends both on the density and on its first derivatives with respect to the…

We study soliton solutions to the Klein-Gordon equation via Lie symmetries and the travelling-wave ansatz. It is shown, by taking a linear combination of the spatial and temporal Lie point symmetries, that soliton solutions naturally exist,…

It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…

Transverse dunes appear in regions of mainly unidirectional wind and high sand availability. A dune model is extended to two dimensional calculation of the shear stress. It is applied to simulate dynamics and morphology of transverse dunes…

A class of generalized nonlinear p-Laplacian evolution equations is studied. These equations model radial diffusion-reaction processes in $n\geq 1$ dimensions, where the diffusivity depends on the gradient of the flow. For this class, all…

We establish a general nonlocal approximation principle for the entropy solutions of scalar conservation laws on $\mathbb{R}$. More precisely, we show that the entropy solution to a nonnegative initial datum can be obtained as a weak-star…

The iconic, deep-MOND-limit (DML) relation between acceleration and mass, $a\sim (M\mathcal{A}_0)^{1/2}/r$, implies that, in MOND, accelerations cannot be linear in the mass distribution ($\mathcal{A}_0\equiv Ga_0$ is the DML constant, and…

In this paper, we consider a general form of nonlinear Schr\"{o}dinger equation with time-dependent nonlinearity. Based on the linear eigenvalue problem, the complete integrability of such nonlinear Schr\"{o}dinger equation is identified by…

An overlooked conservation law for near-inertial waves propagating in a steady background flow provides a new perspective on the concentration of these waves in regions of anticyclonic vorticity. The conservation law implies that this…

We consider chiral fluids within the standard framework of a chiral-invariant underlying field theory, anomalous in presence of electromagnetic fields. Apart from the Noether axial current of the underlying theory, in the limit of ideal…

For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…

We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a…

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…

We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with…