Results 11 to 20 of about 8,875,167 (275)
A New Blow-Up Criterion for the DGH Equation [PDF]
Abstract and Applied Analysis, 2012 We investigate the DGH equation. Analogous to the Camassa-Holm equation, this equation possesses the blow-up phenomenon. We establish a new blow up criterion on the initial data to guarantee the formulation of singularities in finite time.
Mingxuan Zhu +2 more
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Blow-Up Criterion of Weak Solutions for the 3D Boussinesq Equations [PDF]
Journal of Function Spaces, 2015 The Boussinesq equations describe the three-dimensional incompressible fluid moving under the gravity and the earth rotation which come from atmospheric or oceanographic turbulence where rotation and stratification play an important role.
Zhaohui Dai +3 more
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A Losing Estimate for the Ideal MHD Equations with Application to Blow‐up Criterion
SIAM Journal on Mathematical Analysis, 2007 In this paper we study the blow‐up criterion of smooth solution to the ideal MHD equations in $\R^n$. By means of the Fourier frequency localization and Bony paraproduct decomposition, we show a losing estimate for the ideal MHD equations and apply it to establish an improved blow‐up criterion of smooth solutions.
Marco Cannone +2 more
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A blow-up criterion for the inhomogeneous incompressible Euler equations
Nonlinear Analysis, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bae, Hantaek, Lee, Woojae, Shin, Jaeyong
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MathematicsIn this paper, we provide a blow-up criterion for the density-dependent incompressible magnetohydrodynamic system with zero viscosity. The proof uses the Lp-method and the Kato–Ponce inequalities in the harmonic analysis.
Kunlong Shi, Jishan Fan, Gen Nakamura
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Blow-up criterion for the 2D Euler-Boussinesq system in terms of temperature [PDF]
Electronic Journal of Differential Equations, 2016 In this article, we study the blow-up slutions for the 2D Euler-Boussinesq equation. In particular, it is shown that if $$ \int_0^{T^*} \sup_{r\geq 2}\frac{\|\Lambda^{1-\alpha} \theta(t)\|_{L^{r}}} {\sqrt{r\log r ...
Chenyin Qin
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Local existence and blow-up criterion for the Boussinesq equations
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1997 SynopsisIn this paper, we prove local existence and uniqueness of smooth solutions of the Boussinesq equations. We also obtain a blow-up criterion for these smooth solutions. This shows that the maximum norm of the gradient of the passive scalar controls the breakdown of smooth solutions of the Boussinesq equations. As an application of this criterion,
Chae, Dongho, Nam, Hee-Seok
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Blow-up criterion of smooth solutions for magneto-micropolar fluid equations with partial viscosity [PDF]
Boundary Value Problems, 2011 In this paper, we investigate the Cauchy problem for the incompressible magneto-micropolar fluid equations with partial viscosity in ℝn(n = 2, 3). We obtain a Beale-Kato-Majda type blow-up criterion of smooth solutions. MSC (2010): 76D03; 35Q35.
Wang Yu-Zhu, Li Yifang, Wang Yin-Xia
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Blow-up criterion for two-dimensional heat convection equations with zero heat conductivity
Electronic Journal of Differential Equations, 2012 In this article we obtain a blow-up criterion of smooth solutions to Cauchy problem for the incompressible heat convection equations with zero heat conductivity in $mathbb{R}^2$.
Yu-Zhu Wang, Zhiqiang Wei
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A Blow-Up Criterion for 3D Compressible Isentropic Magnetohydrodynamic Equations with Vacuum
MathematicsIn this paper, we investigate a blow-up criterion for compressible magnetohydrodynamic equations. It is shown that if density and velocity satisfy (∥ρ∥L∞(0,T;L∞)+∥u∥C([0,T];L3)
Shujuan Wang, Jialin Ren, Rijian Su
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