scholarly journals Global Solutions to the Oldroyd-B Model with a Class of Large Initial Data

2016 ◽  
Vol 48 (2) ◽  
pp. 1054-1084 ◽  
Author(s):  
Daoyuan Fang ◽  
Ruizhao Zi
Keyword(s):  
Initial Data ◽  
Global Solutions ◽  
Large Initial Data

Global solutions to a hyperbolic-parabolic coupled system with large initial data

2009 ◽  
Vol 29 (3) ◽  
pp. 629-641 ◽  
Author(s):  
Guo Jun ◽  
Xiao Jixiong ◽  
Zhao Huijiang ◽  
Zhu Changjiang
Keyword(s):  
Initial Data ◽  
Global Solutions ◽  
Coupled System ◽  
Large Initial Data

Finite time blow-up of complex solutions of the conserved Kuramoto–Sivashinsky equation in ℝd and in the torus 𝕋d, d ⩾ 1

2019 ◽  
Vol 149 (5) ◽  
pp. 1175-1188
Author(s):  
Léo Agélas
Keyword(s):  
Sobolev Space ◽  
Initial Data ◽  
Besov Space ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Large Initial Data ◽  
Complex Solutions ◽  
Complex Valued ◽  
Sivashinsky Equation

AbstractWe consider complex-valued solutions of the conserved Kuramoto–Sivashinsky equation which describes the coarsening of an unstable solid surface that conserves mass and that is parity symmetric. This equation arises in different aspects of surface growth. Up to now, the problem of existence and smoothness of global solutions of such equations remained open in ℝd and in the torus 𝕋d, d ⩾ 1. In this paper, we answer partially to this question. We prove the finite time blow-up of complex-valued solutions associated with a class of large initial data. More precisely, we show that there is complex-valued initial data that exists in every Besov space (and hence in every Lebesgue and Sobolev space), such that after a finite time, the complex-valued solution is in no Besov space (and hence in no Lebesgue or Sobolev space).

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