Related papers: A remark on a stability criterion for the radial c…
The general stability criteria of inviscid Taylor-Couette flows with angular velocity $\Omega(r)$ are obtained analytically. First, a necessary instability criterion for centrifugal flows is derived as $\xi'(\Omega-\Omega_s)<0$ (or…
Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate…
A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with…
Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressions on tuples of matrices. This interpretation extends their…
We prove infinitesimal rigidity and integrability of the moduli space for Hermitian gravitational instantons. Together with the recent proof by Biquard, Gauduchon, and LeBrun of local rigidity for Hermitian instantons, this completes the…
We consider the most minimal scale invariant extension of the standard model that allows for successful radiative electroweak symmetry breaking and inflation. The framework involves an extra scalar singlet, that plays the r\^ole of the…
In this paper, we establish $\varepsilon$-regularity criteria at one scale for suitable weak solutions to the five dimensional stationary incompressible Navier-Stokes equations in both the unit ball $B_1$ and the unit half ball $B_1^+$,…
In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability…
Homogeneous oscillations of the inflaton after inflation can be unstable to small spatial perturbations even without coupling to other fields. We show that for inflaton potentials $\propto |\phi|^{2n}$ near $|\phi|=0$ and flatter beyond…
Given a map $\phi:X\rightarrow Y$ between $F$-analytic manifolds over a local field $F$ of characteristic $0$, we introduce an invariant $\epsilon_{\star}(\phi)$ which quantifies the integrability of pushforwards of smooth compactly…
Nonlinear two-dimensional internal gravity waves (IGWs) in the atmospheres of the Earth and the Sun are studied. The resulting two-dimensional nonlinear equation has the form of a generalized nonlinear Schr\"{o}dinger equation with nonlocal…
We determine the modulational stability of standing waves with small group velocity in quasi-onedimensional systems slightly above the threshold of a supercritical Hopf bifurcation. The stability limits are given by two different…
In this manuscript we first give the explicit variational structure of the nonlinear elastic waves for isotropic, homogeneous, hyperelastic materials in 2-D. Based on this variational structure, we suggest a null condition which is a kind…
We apply round-off to planar rotations, obtaining a one-parameter family of invertible maps of a two-dimensional lattice. As the angle of rotation approaches pi/2, the fourth iterate of the map produces piecewise-rectilinear motion, which…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous applied and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which…
In this note, we show that the solution to the Dirichlet problem for the minimal surface system in any codimension is unique in the space of distance-decreasing maps. This follows as a corollary of the following stability theorem: if a…
For a domain $\Omega \subset \mathbb{R}^n$ and a small number $\frak{T} > 0$, let \[ \mathcal{E}_0(\Omega) = \lambda_1(\Omega) + {\frak{T}} {\text{tor}}(\Omega) = \inf_{u, w \in H^1_0(\Omega)\setminus \{0\}} \frac{\int |\nabla u|^2}{\int…
As is well known, classical PID control is ubiquitous in industrial processes, yet a rigorous and explicit design theory for nonlinear uncertain MIMO second-order systems remains underdeveloped. In this paper we consider a class of such…
Characterizing existence or not of periodic orbit is a classical problem and it has both theoretical importance and many real applications. Here, several new criterions on nonexistence of periodic orbits of the planar dynamical system $\dot…
Gronwall-Bellman type inequalities entail the following implication: if a sufficiently integrable function satisfies a certain homogeneous linear integral inequality, then it is nonpositive. We present a minimal (necessary and sufficient)…