Local well-posedness and blow-up criterion for a compressible Navier-Stokes-Fourier-P 1 approximate model arising in radiation hydrodynamics

2017 ◽  
Vol 40 (18) ◽  
pp. 6987-6997 ◽  
Author(s):  
Jishan Fan ◽  
Fucai Li ◽  
Gen Nakamura
Keyword(s):  
Blow Up ◽  
Approximate Model ◽  
Navier Stokes ◽  
Radiation Hydrodynamics ◽  
Well Posedness ◽  
Blow Up Criterion

scholarly journals Notes on the Global Well-Posedness for the Maxwell-Navier-Stokes System

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ensil Kang ◽  
Jihoon Lee
Keyword(s):  
Global Existence ◽  
Stokes System ◽  
Blow Up ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Well Posedness ◽  
Regular Solutions ◽  
2D System ◽  
Blow Up Criterion

Masmoudi (2010) obtained global well-posedness for 2D Maxwell-Navier-Stokes system. In this paper, we reprove global existence of regular solutions to the 2D system by using energy estimates and Brezis-Gallouet inequality. Also we obtain a blow-up criterion for solutions to 3D Maxwell-Navier-Stokes system.

Well-posedness and blow-up criterion for the Chaplygin gas equations in ℝN

2019 ◽  
Vol 16 (04) ◽  
pp. 639-661 ◽  
Author(s):  
Zhen Wang ◽  
Xinglong Wu
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Initial Density ◽  
Chaplygin Gas ◽  
Bmo Space ◽  
Well Posedness ◽  
Dimension Formula ◽  
The Cauchy Problem ◽  
Bounded Below ◽  
Blow Up Criterion

We establish a well-posedness theory and a blow-up criterion for the Chaplygin gas equations in [Formula: see text] for any dimension [Formula: see text]. First, given [Formula: see text], [Formula: see text], we prove the well-posedness property for solutions [Formula: see text] in the space [Formula: see text] for the Cauchy problem associated with the Chaplygin gas equations, provided the initial density [Formula: see text] is bounded below. We also prove that the solution of the Chaplygin gas equations depends continuously upon its initial data [Formula: see text] in [Formula: see text] if [Formula: see text], and we state a blow-up criterion for the solutions in the classical BMO space. Finally, using Osgood’s modulus of continuity, we establish a refined blow-up criterion of the solutions.

scholarly journals On the Well-Posedness of the Boussinesq Equation in the Triebel-Lizorkin-Lorentz Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Zhaoyin Xiang ◽  
Wei Yan
Keyword(s):  
Boussinesq Equation ◽  
Blow Up ◽  
Boussinesq Equations ◽  
Lorentz Spaces ◽  
Well Posedness ◽  
Smooth Solutions ◽  
Blow Up Criterion

We establish the local well-posedness and obtain a blow-up criterion of smooth solutions for the Boussinesq equations in the framework of Triebel-Lizorkin-Lorentz spaces. The main ingredients of our proofs are Littlewood-Paley decomposition and the paradifferential calculus.

Some remarks on the paper “On the blow up criterion of 3D Navier–Stokes equations” by J. Benameur

2014 ◽  
Vol 352 (11) ◽  
pp. 913-915 ◽  
Author(s):  
Pablo Braz e Silva ◽  
Wilberclay G. Melo ◽  
Paulo R. Zingano
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Blow Up Criterion
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