Related papers: Point defects in 2-D liquid crystals with singular…
We study stability of solitary wave solutions for the fractional generalized Korteweg-de Vries equation $$ \partial_t u- \partial_{x_1} D^{\alpha}u+ \tfrac{1}{m}\partial_{x_1}(u^m)=0, ~ (x_1,\dots,x_d)\in \mathbb{R}^d, \, \, t\in…
The properties of liquid crystals can be modelled using an order parameter which describes the variability of the local orientation of rod-like molecules. Defects in the director field can arise due to external factors such as applied…
We examine the convective stability of hydrodynamic discs with full stratification in the local approximation and in the presence of thermal diffusion (or relaxation). Various branches of the relevant axisymmetric dispersion relation…
Radial mode stability is a necessary condition for the astrophysical viability of compact objects. In recent years, astrophysical models with two fluids have gain popularity, especially in their ability to model dark matter admixed neutron…
We address the existence and stability of one-dimensional (1D) holes and kinks and two-dimensional (2D) vortex-holes nested in extended binary Bose mixtures, which emerge in the presence of Lee-Huang-Yang (LHY) quantum corrections to the…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
In this paper we address some questions about symmetry, radial monotonicity, and uniqueness for a semilinear fourth-order boundary value problem in the ball of $\mathbb R^2$ deriving from the Kirchhoff-Love model of deformations of thin…
We prove a definitive theorem on the asymptotic stability of point vortex solutions to the full Euler equation in 2 dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex…
Linear stability analysis of the axisymmetric interface of velocity and density discontinuity in rotating gaseous disk has been performed numerically and analytically. Physical mechanisms leading to development of centrifugal and…
We consider the symmetry-breaking steady state bifurcation of a spatially-uniform equilibrium solution of E(2)-equivariant PDEs. We restrict the space of solutions to those that are doubly-periodic with respect to a square or hexagonal…
Defects arise when nematic liquid crystals are under topological constraints at the boundary. Recently the study of defects has drawn a lot of attention. In this paper, we investigate the relationship between two-dimensional defects and…
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial…
Defects are inevitably present in two-dimensional (2D) materials and usually govern their various properties. Here a comprehensive density functional theory-based investigation of 7 kinds of point defects in a recently produced {\gamma}…
We study the stability of standing wave solutions to a one-dimensional Gross-Pitaevsky equation with a periodic potential. We use some simple complex analysis and the Hamiltonian structure of the problem to give a simple rigorous criterion…
We investigate properties of stationary aligned and unaligned spiral perturbation configurations in a composite system of gravitationally coupled stellar and gaseous singular isothermal disks (SIDs) using the two-fluid formalism. We obtain…
Defects in liquid crystals are of great practical importance and theoretical interest. Despite tremendous efforts, predicting the location and transition of defects under various topological constraint and external field remains to be a…
We examine the minimal magnitude of perturbations necessary to change the number $N$ of static equilibrium points of a convex solid $K$. We call the normalized volume of the minimally necessary truncation robustness and we seek shapes with…
We devote this paper to study semi-stable nonconstant radial solutions of $S_k(D^2u) = w(|x|)g(u)$ on the Euclidean space $R^n$. We establish pointwise estimates and necessary conditions for the existence of such solutions (not necessarily…
We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $\theta$. We find an intriguing relationship between the stability and existence conditions for all level-1…
We solve the static isoperimetric problem underlying the Mandelstam-Tamm bound. Among one-dimensional confining potentials with a fixed spectral gap, we prove that the harmonic trap is the unique maximizer of the ground-state position…