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We show that finite element discretizations of incompressible flow problems can be designed to ensure preservation/dissipation of kinetic energy not only globally but also locally. In the context of equal-order (piecewise-linear)…
We introduce a symmetrization of a one-velocity two-pressures Baer-Nunziato type model for mixtures of barotropic compressible fluids. It allows us to justify the zero compaction viscosity limit and to recover a solution of the so-called…
Complex fluids transition from laminar to transitory flow above a critical control parameter, akin to their Newtonian counterparts. In a continuum mechanics sense, fluid elements follow the ensuing complex trajectories, giving rise to…
We prove the existence of the set of ground states in a suitable energy space $\Sigma^s=\{u: \int_{\mathbb{R}^N} \bar{u}(-\Delta+m^2)^s u+V |u|^2<\infty\}$, $s\in (0,\frac{N}{2})$ for the mass-subcritical nonlinear fractional Hartree…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Hamiltonian structure and we then observe…
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that…
In present paper, an analysis of the stability behaviour of ideal efficient solutions to parametric vector optimization problems is conducted. A sufficient condition for the existence of ideal efficient solutions to locally perturbed…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized…
Inspired by work of Colding-Minicozzi on mean curvature flow, Zhang introduced a notion of entropy stability for harmonic map flow. We build further upon this work in several directions. First we prove the equivalence of entropy stability…
The linear stability of the homogeneous equilibrium of non-relativistic fluids with mass flux and special relativistic fluids with the absolute value of the energy vector as internal energy is investigated. It is proved that the equilibrium…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
We give a singular control approach to the problem of minimizing an energy functional for measures with given total mass on a compact real interval, when energy is defined in terms of a completely monotone kernel. This problem occurs both…
In this note we consider the motion of a solid body in a two dimensional incompressible perfect fluid. We prove the global existence of solutions in the case where the initial vorticity belongs to $L^p$ with $p>1$ and is compactly…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
We examine the revenue maximizing loading for the single voyage of a cargo vessel where metacentric stability is taken into account. We formulate the problem as a maximization of a linear function with two linear and one quadratic…
Geometric analysis of steady pseudo-plane ideal flow reveals a fundamental relation between vertical coherence and streamline topology. It shows vertical alignment only exists in straightline jet and circular vortex. A geometric stability…
The point vortex system is usually considered as an idealized model where the vorticity of an ideal incompressible two-dimensional fluid is concentrated in a finite number of moving points. In the case of a single vortex in an otherwise…