相关论文: Blow-ups and modifications of lcK spaces

We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension 1, multiplicity 4, Euler characteristic 2, and first Chern class (2, 2), is the blow-up at two points of a certain hypersurface in a weighted…

The main goal of this paper is to show that the blow up phenomenon (the explosion of the $ \rL^{\infty }$-norm) of the solutions of several classes of evolution problems can be controlled by means of suitable global controls $\alpha (t)$…

We consider two compacta with minimal non-elementary convergence actions of a countable group. When there exists an equivariant continuous map from one to the other, we call the first a blow-up of the second and the second a blow-down of…

A version of the singular Yamabe problem in smooth domains in a closed manifold yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study the blow-up phenomena of Ricci curvatures of these metrics…

We analyze finite-time blowup scenarios of locally self-similar type for the inviscid generalized surface quasi-geostrophic equation (gSQG) in $\mathbb{R}^2$. Under an $L^r$ growth assumption on the self-similar profile and its gradient, we…

For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions as far as blowup points are either regular points or non-quantized singular sources. In particular the uniqueness result…

Let $k$ be an algebraically closed field and let $b$ and $n$ be integers with $n\geq 3$ and $1\leq b \leq n-1.$ Consider the moduli space $X$ of hypersurfaces in $\mathbb{P}^n_k$ of fixed degree $l$ whose singular locus is at least…

For each variety in positive characteristic, there is a series of canonically defined blowups, called F-blowups. We are interested in the question of whether the $e+1$-th blowup dominates the $e$-th, locally or globally. It is shown that…

A degenerate fourth-order parabolic equation modeling condensation phenomena related to Bose-Einstein particles is analyzed. The model is a Fokker-Planck-type approximation of the Boltzmann-Nordheim equation, only keeping the leading order…

In this paper we discuss log blow-up's, introduced by Kazuya Kato, and define the concept of log modifications. Using this concept we prove that any morphism f: X ---> Y of locally noetherian fs log schemes with underlying structures of f…

We investigate the natural involutive structure on the blow-up of ${\Bbb R}^n$ in ${\Bbb C}^n$ extending the complex structure on the complement of the exceptional hypersurface. Our main result is that this structure is hypocomplex, meaning…

We study the possibility of finite-time blow-up for a two dimensional Broadwell model. In a set of rescaled variables, we prove that no self-similar blow-up solution exists, and derive some a priori bounds on the blow-up rate. In the final…

We present an extension of the Randall--Sundrum model in which, due to spontaneous Lorentz symmetry breaking, graviton mixes with bulk vector fields and becomes quasilocalized. The masses of KK modes comprising the four-dimensional graviton…

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper…

For the focusing cubic wave equation, we find an explicit, non-trivial self-similar blowup solution $u^*_T$, which is defined on the whole space and exists in all supercritical dimensions $d \geq 5$. For $d=7$, we analyze its stability…

We construct a solution for the Complex Ginzburg-Landau equation in some critical case, which blows up in finite time $T$ only at one blow-up point. We also give a sharp description of its profile. The proof relies on the reduction of the…

In \cite{JB1}, Benameur proved a blow-up result of the non regular solution of $(NSE)$ in the Sobolev-Gevrey spaces. In this paper we improve this result, precisely we give an exponential type explosion in Sobolev-Gevrey spaces with less…

We establish the first complete classification of finite-time blow-up scenarios for strong solutions to the three-dimensional incompressible Euler equations with surface tension in a bounded domain possessing a closed, moving free boundary.…

In this paper we consider a porous-elastic system consisting of nonlinear boundary/interior damping and nonlinear boundary/interior sources. Our interest lies in the theoretical understanding of the existence, finite time blow-up of…

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…