相关论文: Uniqueness for bubbling solutions with collapsing …

We consider a coagulation multiple-fragmentation equation, which describes the concentration $c\_t(x)$ of particles of mass $x \in (0,\infty)$ at the instant $t \geq 0$ in a model where fragmentation and coalescence phenomena occur. We…

We develop a bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular we show that convergence always occurs with multiplicity one, which…

Five-dimensional cosmological models with two 3-branes and with a buck cosmological constant are studied. It is found that for all the three cases ($\Lambda =0$, $\Lambda >0$, and $\Lambda <0$), the conventional space-time singularity ``big…

In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and…

We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…

We analyze the Rayleigh equation for the collapse of an empty bubble and provide an explanation for some recent analytical approximations to the model. We derive the form of the singularity at the second boundary point and discuss the…

We establish uniqueness and regularity results for tangent cones (at a point or at infinity) with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In…

We consider the five-dimensional supergravity path integral that computes a supersymmetric index, and uncover a wealth of semiclassical saddles with bubbling topology. These are complex finite-temperature configurations asymptotic to…

In the thin wall approximation, we study a class of asymptotically AdS black holes which contain a spherically symmetric vacuum bubble with a different (positive or negative) cosmological constant. Collapsing, expanding, and static bubble…

According to the Belinskii-Khalatnikov-Lifshitz scenario, a collapsing universe approaching a spacelike singularity can be approximated by homogeneous cosmological dynamics, but only if asymptotically small spatial regions are considered.…

A simple model for a scalar field and gravity admits homogeneous isotropic cosmological solutions which cross the Big Bang singularity. In the scaling frame with field dependent effective Planck mass these solutions are regular. They become…

We characterize a singularity in the equal-time three-point density correlations that is generic to two-dimensional interacting Fermi liquids. In momentum space where the three-point correlation is determined by two wavevectors…

For a singular Liouville equation, it is plausible that a non-simple blowup phenomenon occurs around a quantized singular pole. The presence of complex blowup profiles of bubbling solutions presents substantial challenges in applications.…

We consider the harmonic map heat flow for maps from the plane taking values in the sphere, under equivariant symmetry. It is known that solutions to the initial value problem can exhibit bubbling along a sequence of times -- the solution…

In this paper, we extend the analysis of the subcritical approximation of the Nirenberg problem on spheres recently conducted in \cite{MM19, MM}. Specifically, we delve into the scenario where the sequence of blowing up solutions exhibits a…

We study the collapse of a massless scalar field coupled to gravity. A class of blackhole solutions are identified. We also report on a class of solutions where collapse starts from a regular spacelike surface but then the collapsing scalar…

According to conventional modelling by general relativity the collapse of radially symmetric gravitating objects may end in a singular state. But by inclusion of potential energy into the energy tensor, which is required to guarantee global…

In this paper, we derive a sharp version of the singular Trudinger-Moser inequality, which was originally established by Adimurthi and Sandeep (Nonlinear Differ. Equ. Appl. 2007). Moreover, extremal functions for those singular…

Multi-centered bubbling solutions are black hole microstate geometries that arise as smooth solutions of 5-dimensional $\mathcal{N}=2$ Supergravity. When these solutions reach the scaling limit, their resulting geometries develop an…

We establish a series of concentration and oscillation estimates for elliptic equations with exponential nonlinearity $e^{u^p}$ in a disc. Especially, we show various new results on the supercritical case $p>2$ which are left open in the…