Related papers: On the mode stability of a self-similar wave map
In this note we consider $W$-shaped map $W_0=W_{s_1,s_2}$ with $\frac {1}{s_1}+\frac {1}{s_2}=1$ and show that eigenvalue 1 is not stable. We do this in a constructive way. For each perturbing map $W_a$ we show the existence of the "second"…
We consider wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere. It is known from the work of Bizo\'n and Biernat \cite{BizBie15} that in the energy-supercritical case, i.e., for $d \geq 3$, this model admits a…
We introduce a new model equation for Stokes gravity waves based on conformal transformations of Euler's equations. The local version of the model equation is relevant for dynamics of shallow water waves. It allows us to characterize the…
We consider the model of modified gravity with dynamical torsion. This model was previously found to have promising stability properties about various backgrounds. Here we study the stability of linear perturbations about the…
The kink stability of self-similar solutions of a massless scalar field with circular symmetry in 2+1 gravity is studied, and found that such solutions are unstable against the kink perturbations along the sonic line (self-similar horizon).…
We address Euler's equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profile. In agreement with the previous numerical results,…
We study the fundamental self-similar solution to the SU(2) sigma model, found by Shatah and Turok-Spergel. We give a rigorous proof for its mode stability. Based on earlier results by the second author, the present paper constitutes the…
In this paper, we investigate the instability of the spherical travelling wave solutions for the Transport-Stokes system in $\mathbb{R}^3$. First, a classical scaling argument ensures instability among all probability measures for the…
We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt…
In this paper we consider a family of generalized Korteweg-de Vries equations and study the linear modulational instability of small amplitude traveling waves solutions. Under explicit non-degeneracy conditions on the dispersion relation,…
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic…
This paper concerns spectral stability of nonlinear waves in KdV-type evolution equations. The relevant eigenvalue problem is defined by the composition of an unbounded self-adjoint operator with a finite number of negative eigenvalues and…
In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition which allows us to prove the global nonlinear asymptotic stability…
We study the full linear perturbations of a homogeneous and isotropic spacetime in the Eddington-inspired Born-Infeld gravity. The stability of the perturbations are analyzed in the Eddington regime. We find that, for positive $\kappa$, the…
We consider a classical problem of linear stability of convective rolls in a plane layer with stress-free horizontal boundaries near the onset of convection. The problem has been studied by a number of authors, who have shown that rolls of…
In this paper, we study transverse linear stability of line solitary waves to the $2$-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in $3$D. In the case where the surface tension is weak or…
We consider corotational wave maps from Minkowski spacetime into the sphere and the equivariant Yang-Mills equation for all energy-supercritical dimensions. Both models have explicit self-similar finite time blowup solutions, which continue…
We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with…
We study linear perturbations around time dependent spherically symmetric solutions in the Lambda_3 massive gravity theory, which self-accelerate in the vacuum. We find that the dynamics of the scalar perturbations depend on the coordinate…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…