相关论文: On Nonlinear Stability of Muskat Bubbles

We establish the well-posedness of a coupled micro-macro parabolic-elliptic system modeling the interplay between two pressures in a gas-liquid mixture close to equilibrium that is filling a porous media with distributed microstructures.…

This paper studies the one-phase Muskat problem driven by gravity and surface tension. The regime considered here is unstable with the fluid on top of a dry region. By a novel approach using a depth-averaged formulation, we derive two…

Global existence for weak solutions to systems of nematic liquid crystals, with non-constant fluid density has been established by several authors. In this paper, we establish the regularity and uniqueness results for solutions to the…

The stability of the hard-sphere icosahedral quasilattice is analyzed using the differential formulation of the generalized effective liquid approximation. We find that the icosahedral quasilattice is metastable with respect to the…

Although standard planar double bubbles are stable in the sense that the second variation of the perimeter functional is non-negative for all area-preserving perturbations the question arises whether they are dynamically stable. By…

In this paper we consider the evolution of two fluid phases in a porous medium. The fluids are separated from each other and also the wetting phase from air by interfaces which evolve in time. We reduce the problem to an abstract evolution…

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…

We prove the orbital stability of soliton solutions for 2D Maxwell--Lorentz system with extended charged particle. The solitons corresponds to the uniform motion and rotation of the particle. We reduce the corresponding Hamilton system by…

In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity \(\beta_\sigma(f_0')\) which encapsulates local monotonicity and…

We present three ways to establish general stability inequalities for various classes of 2-immersions in Euclidean spaces of higher codimension

The absence, so far, of any graviton signatures at the LHC imposes severe constraints on the Randall-Sundrum scenario. Although a generalization to higher dimensions with nested warpings has been shown to avoid these constraints, apart from…

As an alternative gravity model we consider an extended Einstein-Maxwell gravity containing a gauge invariance property. Extension is assumed to be addition of a directional coupling between spatial electromagnetic fields with the Ricci…

We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the free boundary Euler equations and discussing the local…

A general model of dialton-Maxwell gravity in two dimensions is investigated. The corresponding one-loop effective action and the generalized $\beta$-functions are obtained. A set of models that are fixed points of the renormalization group…

In this work, we present preliminary results of a global fit of the type-II two-Higgs-doublet model (2HDM) with the tool $\texttt{GAMBIT}$. Our study includes various constraints, including the theoretical constraints (unitarity,…

The stability of two bubbles rising initially in-line through a viscous liquid is revisited using a global linear stability analysis formulated within an Arbitrary Lagrangian-Eulerian framework, complemented by fully resolved Embedded…

We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…

Gravitational clustering in the nonlinear regime remains poorly understood. Gravity dual of gravitational clustering has recently been proposed as a means to study the nonlinear regime. The stable clustering ansatz remains a key ingredient…

In this paper, we study the two dimensional Peskin problem with general elasticity law. Specifically, we prove global regularity for small perturbations, in suitable critical spaces, of the circle solution, possibly containing corners. For…

A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…