scholarly journals Finite time blow-up for the Yang-Mills heat flow in higher dimensions

2001 ◽  
Vol 237 (2) ◽  
pp. 321-333 ◽  
Author(s):  
Joseph F. Grotowski
Keyword(s):  
Heat Flow ◽  
Finite Time ◽  
Blow Up ◽  
Higher Dimensions ◽  
Yang Mills

scholarly journals Finite-time blow-up of the heat flow of harmonic maps from surfaces

1992 ◽  
Vol 36 (2) ◽  
pp. 507-515 ◽  
Author(s):  
Kung-Ching Chang ◽  
Wei Yue Ding ◽  
Rugang Ye
Keyword(s):  
Heat Flow ◽  
Finite Time ◽  
Blow Up ◽  
Harmonic Maps

Finite-time blow-up for the heat flow of pseudoharmonic maps

2015 ◽  
Vol 64 (2) ◽  
pp. 441-470 ◽  
Author(s):  
Ting-hui Chang ◽  
Shu-Cheng Chang
Keyword(s):  
Heat Flow ◽  
Finite Time ◽  
Blow Up

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.

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