Related papers: Stability criteria for the 2D $\alpha$-Euler equat…
In this note we formulate recent stability results for Hardy inequalities in the language of Folland and Stein's homogeneous groups. Consequently, we obtain remainder estimates for Rellich type inequalities on homogeneous groups. Main…
We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar…
This paper presents original and close to optimal stability conditions linking the time step and the space step, stronger than the CFL criterion: $\delta t\leq C\delta x^\alpha$ with $\alpha=\frac{2r}{2r-1}$, $r$ an integer, for some…
We study 2D Euler equations on a rotating surface, subject to the effect of the Coriolis force, with an emphasis on surfaces of revolution. We bring in conservation laws that yield long time estimates on solutions to the Euler equation, and…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…
This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy…
We examine the weighted elliptic system \begin{equation*} \begin{cases} -\Delta u=(1+|x|^2)^{\frac{\alpha}{2}} v,\\ -\Delta v=(1+|x|^2)^{\frac{\alpha}{2}} u^p, \end{cases} \quad \mbox{in}\;\ \mathbb{R}^N, \end{equation*}where $N \ge 5$,…
We define a new notion of "b-stability" for a polarised algebraic variety, adapted to the existence problem for Kahler-Einstein metrics on Fano manifolds.
We study the stability/instability of standing waves for the one dimensional nonlinear Schr\"odinger equation with double power nonlinearities: \begin{align*} &i\partial_t u +\partial_x^2 u -|u|^{p-1}u +|u|^{q-1}u=0, \quad (t,x)\in…
The Lane-Emden inequality controls $\iint_{\mathbb{R}^{2d}}\rho(x)\rho(y)|x-y|^{-\lambda}\,dx\,dy$ in terms of the $L^1$ and $L^p$ norms of $\rho$. We provide a remainder estimate for this inequality in terms of a suitable distance of…
We study stability and bifurcations in holomorphic families of polynomial automorphisms of C^2. We say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there. We first show that this defines…
We establish the nonlinear stability to the future of tilted two-fluid Bianchi I solutions to the Einstein-Euler equations with positive cosmological constant and linear equations of state…
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
In this article we study stability aspects for the determination of time-dependent vector and scalar potentials in relativistic Schr\"odinger equation from partial knowledge of boundary measurements. For space dimensions strictly greater…
The second-grade fluid equations are a model for viscoelastic fluids, with two parameters: $\alpha > 0$, corresponding to the elastic response, and $\nu > 0$, corresponding to viscosity. Formally setting these parameters to $0$ reduces the…
This study deals with the Ulam stability of non-autonomous linear differential systems without assuming the condition that they admit an exponential dichotomy. In particular, the best (minimal) Ulam constants for two-dimensional…
Symmetric and antisymmetric terms have been obtained in the framework of the variational approach for two-dimensional (2D) Coulomb systems of symmetric trions XXY. Stability diagrams and certain anomalies arising in the 2D space are…
In this paper, kinds of Schr\"{o}dinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered. By using the concentration compactness principle, the sharp Gagliardo-Nirenberg…
We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…