Related papers: Addendum: 2D homogeneous solutions to the Euler eq…
We discuss general bosonic stationary configurations of N=2, D=4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special…
The nonlinear Schr\"odinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schr\"odinger equation as well as more exotic solutions such as solitary waves…
This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations…
In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
We have previously formulated a simple criterion for deducing the intervals of oscillations in the solutions of second-order linear homogeneous differential equations. In this work, we extend analytically the same criterion to the cubic…
In this paper we present a formally fourth-order accurate hybrid-variable method for the Euler equations in the context of method of lines. The hybrid-variable (HV) method seeks numerical approximations to both cell-averages and nodal…
This paper is devoted to study the Lie algebra of linear symmetries of a homogenous 2nd order ODE, by the method of Kushner, Lychagin and Robstov.
In Ann. Math., 170 (2009), 1417-1436, C. De Lellis and L. Sz\'ekelyhidi Jr. constructed wild solutions of the incompressible Euler equations using a reformulation of the Euler equations as a differential inclusion together with convex…
We develop a second order well-balanced finite volume scheme for compressible Euler equations with a gravitational source term. The well-balanced property holds for arbitrary hydrostatic solutions of the corresponding Euler equations…
Equilibria of binary neutron stars in close circular orbits are computed numerically in a waveless formulation: The full Einstein-relativistic-Euler system is solved on an initial hypersurface to obtain an asymptotically flat form of the…
We propose and analyze a variation of the Euler scheme for state constrained ordinary differential inclusions under weak assumptions on the right-hand side and the state constraints. Convergence results are given for the space-continuous…
We prove the existence of nonradial classical solutions to the 2D incompressible Euler equations with compact support. More precisely, for any positive integer $k$, we construct compactly supported stationary Euler flows of class…
In this paper, we present rotational and self-similar solutions for the compressible Euler equations in R^3 using the separation method. These solutions partly complement Yuen's irrotational and elliptic solutions in R^3 [Commun. Nonlinear…
We extend the formalism of the statistical theory developed for the 2D Euler equation to the case of shallow water system. Relaxation equations towards the maximum entropy state are proposed, which provide a parametrization of sub-grid…
This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system consists of two equations involving one independent variable…
In order to inherit numerically the ergodicity of the damped stochastic nonlinear Schr\"odinger equation with additive noise, we propose a fully discrete scheme, whose spatial direction is based on spectral Galerkin method and temporal…
We consider the Euler scheme for stochastic differential equations with jumps, whose intensity might be infinite and the jump structure may depend on the position. This general type of SDE is explicitly given for Feller processes and a…
We develop computer-assisted tools to study semilinear equations of the form \begin{equation*} -\Delta u -\frac{x}{2}\cdot \nabla{u}= f(x,u,\nabla u) ,\quad x\in\mathbb{R}^d. \end{equation*} Such equations appear naturally in several…
This note concerns stationary solutions of the Euler equations for an ideal fluid on a closed 3-manifold. We prove that if the velocity field of such a solution has no zeroes and real analytic Bernoulli function, then it can be rescaled to…