相关论文: On Nonlinear Stability of Muskat Bubbles

The property of adiabatic invariance is studied for the generalized potential satisfying the condition of identity of sphere's and point mass's gravity. That function contains a second term corresponding to the cosmological constant as…

This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done…

The physics of membranes, a classic subject, acquires new momentum from two-dimensional (2D) materials multilayers. This work reports the surprising results emerged during a theoretical study of equilibrium geometry of bilayers as…

A recently proposed theory of modified gravity with an explicit ``anomalous'' coupling of the Ricci curvature to matter is discussed, and an inequality is derived which expresses a necessary and sufficient condition to avoid the notorius…

In this paper, we prove that if a solution to the Muskat problem with different densities and the same viscosity is sufficiently smooth, the solution is analytic in a region that degenerates at the turnover points, provided some additional…

We propose a model for modified gravity that meets the conditions of viability. The model has stable constant curvature solution and for an special case contains flat space time solution. The model also leads to matter stability under small…

Taking advantage of the competition between elasticity and capillarity has proven to be an efficient way to design structures by folding, bending, or assembling elastic objects in contact with liquid interfaces. Elastocapillary effects…

This paper is concerned with the global well-posedness of the two-dimensional incompressible vorticity equation in the half plane. Under the assumption that the initial vorticity $\omega_0\in W^{k,p}(\R^{2}_+)$ with $k\geq3$ and $1<p<2$, it…

In the current review, we provide a summary of the recent progress made in the cosmological aspect of extra-dimensional Lovelock gravity. Our review covers a wide variety of particular model/matter source combinations:…

We study the Boltzmann equation near vacuum in anisotropic low-regularity Besov spaces. We establish the global existence and uniqueness of strong solutions with the critical regularity index $2/p$ for $p\in[1,\infty)$ in $\mathbb{R}^3$.…

A recently introduced approach for the dynamical analysis and quantization of field theoretical models with second class constraints is ilustrated applied to linearized gravity in 3-D. The canonical structure of two different models of…

We study the Muskat problem describing the vertical motion of two immiscible fluids in a two-dimensional homogeneous porous medium in an $L_p$-setting with $p\in(1,\infty)$. The Sobolev space $W^s_p(\mathbb{R})$ with $s=1+1/p$ is a critical…

In this paper, we discuss with the global well-posedness of 2D anisotropic nonlinear Boussinesq equations with any two positive viscosities and one positive thermal diffusivity. More precisely, for three kinds of viscous combinations, we…

We investigate the gravitational behavior of spherical domain walls (bubbles) arising during the phase transitions in the early Universe. In the thin-wall approximation we show the existence of the new solution of Einstein equations with…

In this paper, we have reviewed the present status of the theory of equilibrium configurations of compact binary star systems in Newtonian gravity. Evolutionary processes of compact binary star systems due to gravitational wave emission can…

We discuss a model which gives rise to cosmic self-acceleration due to modified gravity. Improvements introduced by this approach are the following: In the coordinate system commonly used, the metric does not grow in the bulk, and no…

The diffusion-driven growth of a dense cloud of bubbles immersed in a gas-supersaturated liquid is a problem that finds applications in several modern technologies such as solvent-exchange micro-reactors, nanotechnology or the manufacturing…

In this contribution we review the ideas and results presented in the articles arXiv:2002.01764 and arXiv:2110.08276 where the decay of AdS vacua into bubbles of nothing is studied. We firstly consider AdS vacua in General Relativity with a…

Motivated by the astrophysical problems of star formations from molecular clouds,we make the first step on the possible long time behaviors of certain irregularly-shaped molecular clouds. We emphasis the main difficulty of the blowups of…

We prove the global well-posedness of the stochastic Abelian-Higgs equations in two dimensions. The proof is based on a new covariant approach, which consists of two parts: First, we introduce covariant stochastic objects. The covariant…