Global Existence, Finite Time Blow-Up, and Vacuum Isolating Phenomenon for a Class of Thin-Film Equation

2019 ◽  
Vol 26 (2) ◽  
pp. 265-288
Author(s):  
Guangyu Xu ◽  
Jun Zhou ◽  
Chunlai Mu
Keyword(s):  
Thin Film ◽  
Global Existence ◽  
Finite Time ◽  
Blow Up ◽  
Thin Film Equation

Global existence blow up and extinction for a class of thin-film equation

2016 ◽  
Vol 147 ◽  
pp. 96-109 ◽  
Author(s):  
Qingwei Li ◽  
Wenjie Gao ◽  
Yuzhu Han
Keyword(s):  
Thin Film ◽  
Global Existence ◽  
Blow Up ◽  
Thin Film Equation

scholarly journals Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongbin Wang ◽  
Binhua Feng
Keyword(s):  
Global Existence ◽  
Finite Time ◽  
Critical Case ◽  
Blow Up ◽  
Critical Mass ◽  
Choquard Equation ◽  
Power Type ◽  
Scale Invariant ◽  
Nonlinear Schrödinger ◽  
Sharp Thresholds

AbstractIn this paper, we consider the sharp thresholds of blow-up and global existence for the nonlinear Schrödinger–Choquard equation $$ i\psi _{t}+\Delta \psi =\lambda _{1} \vert \psi \vert ^{p_{1}}\psi +\lambda _{2}\bigl(I _{\alpha } \ast \vert \psi \vert ^{p_{2}}\bigr) \vert \psi \vert ^{p_{2}-2}\psi . $$iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. We derive some finite time blow-up results. Due to the failure of this equation to be scale invariant, we obtain some sharp thresholds of blow-up and global existence by constructing some new estimates. In particular, we prove the global existence for this equation with critical mass in the $L^{2}$L2-critical case. Our obtained results extend and improve some recent results.

scholarly journals Global existence for a thin film equation with subcritical mass

2017 ◽  
Vol 22 (4) ◽  
pp. 1461-1492 ◽  
Author(s):  
Jian-Guo Liu ◽  
◽  
Jinhuan Wang ◽  
Keyword(s):  
Thin Film ◽  
Global Existence ◽  
Thin Film Equation
Sign in / Sign up

Export Citation Format

Share Document