相关论文: Globally stable blowup profile for supercritical w…

We show that wave maps $\phi$ from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces $\H^m$ are globally smooth in time if the initial data is smooth, conditionally on some reasonable claims concerning the local theory of such…

We investigate the finite-time blow-up of solutions to a Tricomi-type equation with scale-invariant potential and power nonlinearities in the oscillatory regime. For smooth, compactly supported, nonnegative initial data, we prove…

Using the harmonic map heat flow, we construct an energy class for wave maps $\phi$ from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces $\H^m$, and then show (conditionally on a large data well-posedness claim for such wave…

We show that the $a$-parameterized family of the generalized Constantin-Lax-Majda model, also known as the Okamoto-Sakajo-Wunsch model, admits exact self-similar finite-time blowup solutions with interiorly smooth profiles for all $a\leq…

In the present work we revisit the problem of the generalized Korteweg-de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergence of blow-up solutions, as traveling waveforms lose their…

We consider the focusing nonlinear Schr\"odinger equation with inverse square potential \[ i\partial_t u + \Delta u + c|x|^{-2} u = - |u|^\alpha u, \quad u(0) = u_0 \in H^1, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, \] where $d \geq…

We study co--rotational wave maps from $(3+1)$--Minkowski space to the three--sphere $S^3$. It is known that there exists a countable family $\{f_n\}$ of self--similar solutions. We investigate their stability under linear perturbations by…

We investigate novel scenarios of self-similar finite-time blowups of the generalized Constantin-Lax-Majda model with a parameter $a$, which are induced by a new setting where the smooth initial data satisfy certain derivative degeneracy…

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation \[ \Box u = -u^5 \] on $\R^{3+1}$ constructed in earlier work by Krieger-Schlag-Tataru are stable along a co-dimension three manifold of…

For Schr\"odinger maps from $\R^2\times\R^+$ to the 2-sphere $\S^2$, it is not known if finite energy solutions can form singularities (``blowup'') in finite time. We consider equivariant solutions with energy near the energy of the…

We consider the semilinear wave equation with subconformal power nonlinearity in two space dimensions. We construct a finite-time blow-up solution with an isolated characteristic blow-up point at the origin, and a blow-up surface which is…

The main objective of this manuscript is to investigate the global behavior of the solutions to the viscoelastic wave equation with a linear memory term of Boltzmann type, and a nonlinear damping modeling friction, as well as a…

The goal for this paper is twofold. Our first main objective is to develop Bahouri-Gerard type profile decompositions for waves on hyperbolic space. Recently, such profile decompositions have proved to be a versatile tool in the study of…

We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution which guarantees stability. Our stability result…

We consider the finite-time blow-up dynamics of solutions to the self-dual Chern-Simons-Schr\"odinger (CSS) equation (also referred to as the Jackiw-Pi model) near the radial soliton $Q$ with the least $L^{2}$-norm (ground state). While a…

In this work we consider the focusing, energy-critical wave equation in 3D radial case. It has been verified that any global or type II blow-up solution decomposes into a superposition of several decoupled grounds states, a free wave and a…

We investigate the axisymmetric incompressible Euler equations without swirl in $\mathbb R^d$ with $d\geq 3$. For any $\alpha\in(0, \alpha_d)$, where $\alpha_d=1-2/d$, we construct a self-similar blow-up solution whose initial velocity…

In this paper we introduce the channel of energy argument to the study of energy critical wave maps into the sphere. More precisely, we prove a channel of energy type inequality for small energy wave maps, and as an application we show that…

The harmonic map heat flow is a geometric flow well known to produce solutions whose gradient blows up in finite time. A popular model for investigating the blow-up is the heat flow for maps $\mathbb R^{d}\to S^{d}$, restricted to…

We consider the semilinear heat equation, to which we add a nonlinear gradient term, with a critical power. We construct a solution which blows up in finite time. We also give a sharp description of its blow-up profile. The proof relies on…