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Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential

Jing Lu — 2013

Applicationes Mathematicae

We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].

Dynamics of a modified Davey-Stewartson system in ℝ³

Jing Lu — 2016

Colloquium Mathematicae

We study the Cauchy problem in ℝ³ for the modified Davey-Stewartson system $i \partial ₜ u + Δ u = λ ₁ | u | ⁴ u + λ ₂ b ₁ u v_{x ₁}$ , $- Δ v = b ₂ {(| u | ²)}_{x ₁}$ . Under certain conditions on λ₁ and λ₂, we provide a complete picture of the local and global well-posedness, scattering and blow-up of the solutions in the energy space. Methods used in the paper are based upon the perturbation theory from [Tao et al., Comm. Partial Differential Equations 32 (2007), 1281-1343] and the convexity method from [Glassey, J. Math. Phys. 18 (1977), 1794-1797].

Quasicontinuous spaces

Jing Lu; Bin Zhao; Kaiyun Wang; Dong Sheng Zhao — 2022

Commentationes Mathematicae Universitatis Carolinae

We lift the notion of quasicontinuous posets to the topology context, called quasicontinuous spaces, and further study such spaces. The main results are: (1) A $T_{0}$ space $(X, τ)$ is a quasicontinuous space if and only if $S I (X)$ is locally hypercompact if and only if $(τ_{S I}, \subseteq)$ is a hypercontinuous lattice; (2) a $T_{0}$ space $X$ is an $S I$ -continuous space if and only if $X$ is a meet continuous and quasicontinuous space; (3) if a $C$ -space $X$ is a well-filtered poset under its specialization order, then $X$ is a quasicontinuous space...

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Currently displaying 1 – 6 of 6

Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential

Dynamics of a modified Davey-Stewartson system in ℝ³

Quasicontinuous spaces

Pseudo-steady-state productivity formula for a partially penetrating vertical well in a box-shaped reservoir.

A new composite implicit iterative process for a finite family of nonexpansive mappings in Banach spaces.

Productivity formulas for a partially penetrating vertical well in a circular cylinder drainage volume.