Related papers: Geometry of Weak Stability Boundaries
We study semilinear rough stochastic partial differential equations as introduced in [Gerasimovi{\v{c}}s, Hairer; EJP 2019]. We provide $\mathcal{L}^p(\Omega)$-integrable a priori bounds for the solution and its linearization in case the…
In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work…
In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most…
A fundamental aspect of the three-body problem is its stability. Most stability studies have focused on the co-planar three-body problem, deriving analytic criteria for the dynamical stability of such pro/retrograde systems. Numerical…
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…
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…
Lyapunov stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of stability…
This paper proposes a systematic method for generating practical and robust low-thrust spacecraft trajectories. One contribution is to consider the change in mass of the spacecraft at two levels: a) the propulsive acceleration and b) the…
Weakly bound states often occur in nuclear physics. To precisely understand their properties, the coupling to the continuum should be worked out explicitely. In a first step, we use a simple nuclear model in the continuum and on a lattice…
We investigate the formation of three-body bound states in the continuum by tracing pole trajectories in the complex energy plane under variation of system parameters. Using a one-dimensional model of two identical bosons and a…
Observational surveys show that at least ~ 30% of short-period multiplanetary systems host tightly packed planets, some of which are locked in stable chains of mean-motion resonances. Despite recent progress, the dynamical stability of…
The article studies the transport equation that governes the motion of a fluid in a bounded domain, under the hypothesis of zero velocity at the boundary and supposing the incompressible nature of the fluid. Together with existence and…
We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…
The aim of this work is to prove the global-in-time existence of weak solutions for a viscoelastic phase separation model in three space dimensions. To this end we apply the relative energy concept provided by [3]. We consider the case of…
We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…
The half-wave maps equation is a nonlocal geometric equation arising in the continuum dynamics of Haldane-Shashtry and Calogero-Moser spin systems. In high dimensions $n\geq4$, global wellposedness for data which is small in the critical…
A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the…
The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the…
The Ekman boundary layer is a fundamental concept in fluid dynamics that describes fluid motion near boundaries affected by Earth's rotation. Most theoretical studies have simplified their analysis by assuming a planar boundary surface,…
We have examined the stability of triangular equilibrium points in Robes's generalised restricted three body problem. The problem is generalised in the sense that more massive primary has been taken as an oblate spheroid. We have found the…