In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on $\mathbb{R}^d$ ($d\geq 5$) with nonradial data. This problem radial assumption was studied by T. Duyckaerts and F. Merle in \cite{DM} $d=3,4,5$ later D. Li X. Zhang \cite{LZ} $d \geq 6$. We generalize conclusion removing $d\geq 5$. A key step is to show exponential convergence ground stat...

We consider a model of galaxy clusters in which the hot gas is in hydrostatic equilibrium and maintains energy balance between radiative cooling and heating by thermal conduction. We analyze the thermal stability of the gas using a Lagrangian perturbation analysis. For thermal conductivity at the level of ∼ 20 − 40% of Spitzer conductivity, consistent with previous estimates for cluster gas, we...

A characterization of the closed principal ideals in nonradial Hörmander algebras of holomorphic functions of several variables in terms of the behaviour of the generator is obtained. This result is applied to study the range of convolution operators and ultradifferential operators on spaces of quasianalytic functions of Beurling type. Contrary to what is known to happen in the case of non-quas...

We consider the following superlinear elliptic equation on S ε∆Snu− u + u = 0 in S, u > 0 in S where ∆Sn is the Laplace-Beltrami operator on S. We prove that for any k = 1, ..., n−1, there exists pk > 1 such that for 1 < p < pk and ε sufficiently small, there exist at least n − k positive solutions concentrating on k−dimensional subset of the equator. We also discuss the problem on geodesic bal...

Mechanisms which produce a mixing in the solar core, based on the original idea of the “solar spoon” (Dilke & Gough 1972), for explaining the neutrino problem have recently been ruled out by Bahcall & Kumar (1993). We therefore revisit the original work of Rosenbluth & Bahcall (1973) on the nonspherical thermal instabilities in the solar core, introducing some improvements. The authors found th...