Related papers: Mass Concentration for the Davey-Stewartson System

In this paper, blowup phenomenon for the semilinear wave equation with time-dependent speed of propagation and scattering damping is considered under the smallness of initial data. Our result contains small data blowup for sub-Strauss…

This paper deals with the finite-time blow-up phenomena of classical solutions for Vlasov/Navier-Stokes equations under suitable assumptions on the initial configurations. We show that a solution to the coupled kinetic-fluid system may be…

We perform the apriori analysis of solutions to critical nonlinear elliptic equations on manifolds with boundary. The solutions are of minimizing type. The originality is that we impose no condition on the boundary, which leads us to assume…

This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…

Using the concentration-compactness method and the localized virial type arguments, we study the behavior of $H^1$ solutions to the focusing quintic NLS in $\R^2$, namely, $$i \partial_t u+\Delta u+|u|^4u=0,\quad\quad (x, t) \in…

In this paper we consider nonnegative solutions of the following parabolic-elliptic cross-diffusion system \begin{equation*} \left\{ \begin{array}{l} \begin{aligned} &u_t = \Delta u - \nabla(u f(|\nabla v|^2 )\nabla v), \\[6pt] &0= \Delta v…

We study the blow-up dynamics for the $L^2$-critical focusing half-wave equation on the real line, a nonlocal dispersive PDE arising in various physical models. As in other mass-critical models, the ground state solution becomes a threshold…

We study positive blowing-up solutions of systems of the form: $$u_t=\delta_1 \Delta u+e^{pv},\quad v_t= \delta_2\Delta v+e^{qu},$$ with $\delta_1,\delta_2>0$ and $p, q>0$. We prove single-point blow-up for large classes of radially…

We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of…

An efficient high precision hybrid numerical approach for integrable Davey-Stewartson (DS) I equations for trivial boundary conditions at infinity is presented for Schwartz class initial data. The code is used for a detailed numerical study…

We consider a mass critical nonlinear Schr\"{o}dinger equation with a real-valued potential. In this work, we construct a minimal mass solution that blows up at finite time, under weaker assumptions on spatial dimensions and potentials than…

In this paper we study dynamical properties of blowup solutions to the focusing intercritical (mass-supercritical and energy-subcritical) nonlinear fourth-order Schr\"odinger equation. We firstly establish the profile decomposition of…

In the last twenty years, there have been significant advances in the study of the blow-up phenomenon for the critical generalized Korteweg-de Vries equation, including the determination of sufficient conditions for blowup, the stability of…

This paper is devoted to the analysis of the classical Keller-Segel system over $\mathbb{R}^d$, $d\geq 3$. We describe as much as possible the dynamics of the system characterized by various criteria, both in the parabolic-elliptic case and…

In this article, we study the two dimensional focusing finitely and infinitely coupled cubic nonlinear Schr\"odinger system when the mass is equal to the scattering threshold. For the focusing finitely coupled cubic nonlinear Schr\"odinger…

For a specific choice of the diffusion, the parabolic-elliptic Patlak-Keller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is…

In this work, we show the existence of ground state solutions for an $l$-component system of non-linear Schr\"{o}dinger equations with quadratic-type growth interactions in the energy-critical case. They are obtained analyzing a critical…

We study the general (2+1)-dimensional Davey-Stewartson (DS) equations with nonlinear and gain terms and acquire explicit solutions through variable separation approach. In particular, we deduce some main novel excitations for the DS…

We study finite-time blow-up for the one-dimensional nonlinear wave equation with a quadratic time-derivative nonlinearity, \[ u_{tt}-u_{xx}=(u_t)^2,\qquad (x,t)\in\mathbb R\times[0,T). \] Building on the work of Ghoul, Liu, and Masmoudi…

We construct a new class of multi-solitary wave solutions for the mass critical two dimensional nonlinear Schrodinger equation (NLS). Given any integer K>1, there exists a global (for positive time) solution of (NLS) that decomposes…