scholarly journals Local existence and blow-up criterion of the ideal density-dependent flows

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Fangyi He ◽  
Jishan Fan ◽  
Yong Zhou
Keyword(s):  
Blow Up ◽  
Local Existence ◽  
Density Dependent ◽  
The Ideal ◽  
Blow Up Criterion

scholarly journals Blow-up criterion for the density dependent inviscid Boussinesq equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Li Li ◽  
Yanping Zhou
Keyword(s):  
Velocity Field ◽  
Energy Method ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Boussinesq Equations ◽  
Smooth Solutions ◽  
Density Dependent ◽  
Priori Estimates ◽  
Blow Up Criterion

Abstract In this work, we consider the density-dependent incompressible inviscid Boussinesq equations in $\mathbb{R}^{N}\ (N\geq 2)$ R N ( N ≥ 2 ) . By using the basic energy method, we first give the a priori estimates of smooth solutions and then get a blow-up criterion. This shows that the maximum norm of the gradient velocity field controls the breakdown of smooth solutions of the density-dependent inviscid Boussinesq equations. Our result extends the known blow-up criteria.

Local existence and Serrin-type blow-up criterion for strong solutions to the radiation hydrodynamic equations

2020 ◽  
Vol 17 (03) ◽  
pp. 501-557
Author(s):  
Hao Li ◽  
Yachun Li
Keyword(s):  
Blow Up ◽  
Initial Density ◽  
Local Existence ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Hydrodynamic Equations ◽  
Open Set ◽  
The Cauchy Problem ◽  
Local Strong Solutions ◽  
Blow Up Criterion

We consider the Cauchy problem for the three-dimensional, compressible radiation hydrodynamic equations. We establish the existence and uniqueness of local strong solutions for large initial data satisfying some compatibility condition. The initial density need not be positive and may vanish in an open set. Moreover, we establish a Serrin-type blow-up criterion, which is stated in terms of the velocity and density variables [Formula: see text] and is independent of the temperature and the radiation intensity.

A Losing Estimate for the Ideal MHD Equations with Application to Blow‐up Criterion

2007 ◽  
Vol 38 (6) ◽  
pp. 1847-1859 ◽  
Author(s):  
Marco Cannone ◽  
Qionglei Chen ◽  
Changxing Miao
Keyword(s):  
Blow Up ◽  
Mhd Equations ◽  
Ideal Mhd ◽  
The Ideal ◽  
Blow Up Criterion

scholarly journals Local existence and blow-up criterion of Hölder continuous solutions of the Boussinesq equations

1999 ◽  
Vol 155 ◽  
pp. 55-80 ◽  
Author(s):  
Dongho Chae ◽  
Sung-Ki Kim ◽  
Hee-Seok Nam
Keyword(s):  
Existence And Uniqueness ◽  
Blow Up ◽  
Local Existence ◽  
Boussinesq Equations ◽  
Passive Scalar ◽  
Continuous Solutions ◽  
Hölder Continuous ◽  
Local Existence And Uniqueness ◽  
Local Solutions ◽  
Blow Up Criterion

AbstractIn this paper we prove the local existence and uniqueness of C1+γ solutions of the Boussinesq equations with initial data υ0, θ0 ∈ C1+γ, ω0, ∇θ0 ∈ Lq for 0 < γ < 1 and 1 < q < 2. We also obtain a blow-up criterion for this local solutions. More precisely we show that the gradient of the passive scalar θ controls the breakdown of C1+γ solutions of the Boussinesq equations.

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