Related papers: Linear stability of elliptic relative equilibria o…
In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three…
A longstanding belief has been that the semimajor axes, in the Newtonian planetary problem, are stable. In the course of the XIX century, Laplace, Lagrange and others gave stronger and stronger arguments in this direction, thus culminating…
A symmetric planar central configuration of the Newtonian six-body problem $x$ is called cross central configuration if there are precisely four bodies on a symmetry line of $x$. We use complex algebraic geometry and Groebner basis theory…
In this paper, we extend the basic model of the restricted four-body problem introducing two bigger dominant primaries $m_1$ and $m_2$ as oblate spheroids when masses of the two primary bodies ($m_2$ and $m_3$) are equal. The aim of this…
The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is…
We establish the well-posedness of a coupled micro-macro parabolic-elliptic system modeling the interplay between two pressures in a gas-liquid mixture close to equilibrium that is filling a porous media with distributed microstructures.…
We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under…
We consider the inverse problem of determining some class of nonlinear terms appearing in an elliptic equation from boundary measurements. More precisely, we study the stability issue for this class of inverse problems. Under suitable…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides…
We prove that if for relative equilibrium solutions of a generalisation of quasi-homogeneous $n$-body problems the masses and rotation are given, then the minimum distance between the point masses of such a relative equilibrium has a…
The Newtonian restricted three-body problem involving a positive primary point mass, $m_+$, and a negative secondary point mass, $m_-$, in a circular orbit, and a positive or negative tertiary point mass, $m_3$, with $m_+ > |m_-| \gg…
For the gravitational $n$-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
In this paper, we present sharp stability results for various reverse isoperimetric problems in $\mathbb R^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for $\lambda$-convex bodies -- convex bodies with…
A stability version of the Blaschke-Santal\'o inequality and the affine isoperimetric inequality for convex bodies of dimension n>2 is proved. The first step is the reduction to the case when the convex body is o-symmetric and has axial…
We investigate the stability of motion close to the Lagrangian equilibrium points L4 and L5 in the framework of the spatial, elliptic, restricted three- body problem, subject to the radial component of Poynting-Robertson drag. For this…
The main objective of this paper is to study the regularity and stability for solutions to the conductivity problems with degenerate coefficients in the presence of two rigid conductors, as one conductor keeps motionless and another…
We consider an isolated system made of two pointlike bodies interacting at a distance in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic mechanics", founded on…
The new concept of a system of hex equations is introduced as an overdetermined system of six five-point face-centered quad equations defined on six vertices of a hexagon. For a consistent system of hex equations, two variables on…