Related papers: Euler equations in a 3+1 framework

We discuss general bosonic configurations of four-dimensional N=2 supergravity coupled to vector multiplets in (t,s) space-time. The supergravity theories with Euclidean and neutral signature are described by the so-called para-special…

We introduce a damping term for the special relativistic Euler equations in $3$-D and show that the equations reduce to the non-relativistic damped Euler equations in the Newtonian limit. We then write the equations as a symmetric…

We establish a result concerning the so-called Lagrangian controllability of the Euler equation for incompressible perfect fluids in dimension 3. More precisely we consider a connected bounded domain of R^3 and two smooth contractible sets…

Our recent result on the construction of perfect fluid equations with N=1,2 Schr\"odinger supersymmetry [Mod. Phys. Lett. A 41 (2026) 2550214] is extended to accommodate nonrelativistic conformal supersymmetries of other types. Two cases…

In the variational principle leading to the Euler equation for a perfect fluid, we can use the method of undetermined multiplier for holonomic constraints representing mass conservation and adiabatic condition. For a dissipative fluid, the…

In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with vaccum. Using the developed Lagrangian flow map formulation, we show a short-time solution for a general pressure law. A…

In recent works, the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how…

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,…

The Euler system in fluid dynamics is a model of a compressible inviscid fluid incorporating the three basic physical principles: Conservation of mass, momentum, and energy. We show that the Cauchy problem is basically ill-posed for the…

This paper contributes to the study of large data problems for $C^1$ solutions of the relativistic Euler equations. In the $(1+1)$-dimensional spacetime setting, if the initial data are away from vacuum, a key difficulty in proving the…

We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group of all smooth and orientation-preserving diffeomorphisms on the circle. These include…

We introduce a natural notion of incompressibility for fluids governed by the relativistic Euler equations on a fixed background spacetime, and show that the resulting equations reduce to the incompressible Euler equations in the classical…

A case can be made that the utility of quasi-linear systems of conservation laws as physical models is largely limited to Euler system models of fluid flow, at least in higher dimensions. Qualified corroboration of this conjecture is…

We consider a complexification of the Euler equations introduced by \v{S}ver\'ak which conserves energy. We prove that these complex Euler equations are nonlinearly ill-posed below analytic regularity and, moreover, we exhibit solutions…

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of…

Euler's transformation formula for the Gauss hypergeometric function 2F1 is extended to hypergeometric functions of higher order. Unusually, the generalized transformation constrains the hypergeometric function parameters algebraically but…

A stochastic Euler equation is proposed, describing the motion of a particle density, forced by the random action of virtual photons in vacuum. After time averaging, the Euler equation is reduced to the Reynolds equation, well studied in…

In this work we extend our previously developed formalism of Newtonian multi-fluid hydrodynamics to allow for coupling between the fluids and the electromagnetic and gravitational field. This is achieved within the convective variational…

We extend classical Euclidean stability theorems corresponding to the nonrelativistic Hamiltonians of ions with one electron to the setting of non parabolic Riemannian 3-manifolds.

This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…