相关论文: A third-order conservation law for the Kirchhoff-P…

In this article we focus our attention on the principle of energy conservation within the context of systems of fluid dynamics. We give an overview of results concerning the resolution of the famous Onsager conjecture - which states…

For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained. Since this approach does not contain approximating…

This paper presents sufficient conditions for the solvability of the third order three point boundary value problem \begin{equation*} \left\{ \begin{array}{c} -u^{\prime \prime \prime }(t)=f(t,\,v(t),\,v^{\prime }(t)) \\ -v^{\prime \prime…

The letter considers non-isothermal fluid flows and revises simplifications of basic hydrodynamic equations for such flows arriving eventually to a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of…

We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential…

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant…

In these notes we discuss the conservation of the energy for weak solutions of the two-dimensional incompressible Euler equations. Weak solutions with vorticity in $L^\infty_t L^p_x$ with $p\geq 3/2$ are always conservative, while for less…

Building on the information-theoretic perspective of P.~D.~Lax [\textit{Proc.\ Sympos., Math.\ Res.\ Center, Univ.\ Wisconsin}, 1978], we establish a two-sided quantitative compactness estimate for numerical solutions of scalar conservation…

Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Here, these concepts are extended to the realm of iterative methods by formally defining locally conservative and flux…

In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by…

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…

The existence of conservation laws is one of the most important requirement of physical theories. Some of them, like energy conservation, knows no experimental exception. However, the generalization of these conservation laws to curved…

We consider mildly degenerate Kirchhoff equations with a small parameter and a weak dissipation term. We prove the existence of global solutions when the parameter is small with respect to the size of initial data. Then we provide…

A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference…

We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…

In this paper we consider a generalized fourth order nonlinear Kirchhoff equation in a bounded domain in $\mathbb R^{N}, N\geq2$ under Navier boundary conditions and with sublinear nonlinearity. We employ a change of variable which reduces…

The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence…

We deal with the 3D inviscid Leray-{\alpha} model. The well posedness for this problem is not known; by adding a random perturbation we prove that there exists a unique (in law) global solution. The random forcing term formally preserves…

We perform the Hamiltonian analysis for the lowest-order effective action, up to second order in derivatives, of the complete Horava theory. The model includes the invariant terms that depend on \partial_i ln N proposed by Blas, Pujolas and…

We present a fully discrete approximation technique for the compressible Navier-Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time…