Related papers: Unstable manifolds of Euler equations
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…
This paper is devoted to the study of rigidity properties for special solutions of nonlinear elliptic partial differential equations on smooth, boundaryless Riemannian manifolds. As far as stable solutions are concerned, we derive a new…
We study some classes of semi-linear differential equations including both well-posed and ill-posed cases that can generate cocycles (or cocycle correspondences with generating cocycles). Under exponential dichotomy condition with other…
A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…
This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…
We derive a new formulation of the relativistic Euler equations that exhibits remarkable properties. This new formulation consists of a coupled system of geometric wave, transport, and elliptic equations, sourced by nonlinearities that are…
The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…
It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space $B^{1/3}_{3,\infty}$. When the singular set of the solution is (or belongs to) a smooth manifold, we…
The stability of a system of $N$ equal sized mutually gravitating spheres resting on each other in a straight line and rotating in inertial space is considered. This is a generalization of the "Euler Resting" configurations previously…
On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…
We study the dynamics of solutions of nonlinear Schr\"odinger equation near unstable ground states. The existence of the local center stable manifold around ground states and the asymptotic stability for the solutions on the manifold is…
We deal with the as yet unresolved exponential stability problem for Beck's Problem on a metric star graph with three identical edges. The edges are stretched Euler--Bernoulli beams which are simply supported with respect to the outer…
We study the stability of new neutral and electrically charged four-dimensional black hole solutions of Einstein's equations with a positive cosmological constant and conformally coupled scalar field. The neutral black holes are always…
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…
While it is well known that constant rotation induces linear dispersive effects in various fluid models, we study here its effect on long time nonlinear dynamics in the inviscid setting. More precisely, we investigate stability in the 3d…
The relativistic Vlasov-Maxwell system describes the evolution of a collisionless plasma. The problem of linear instability of this system is considered in two physical settings: the so-called "one and one-half" dimensional case, and the…
Some exotic compact objects possess evanescent ergosurfaces: timelike submanifolds on which a Killing vector field, which is timelike everywhere else, becomes null. We show that any manifold possessing an evanescent ergosurface but no event…
We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is…
The high-order accuracy of Fourier method makes it the method of choice in many large scale simulations. We discuss here the stability of Fourier method for nonlinear evolution problems, focusing on the two prototypical cases of the…
A map which is non-orientable or has non-empty boundary has a canonical double cover which is orientable and has empty boundary. The map is called stable if every automorphism of this cover is a lift of an automorphism of the map. This note…