scholarly journals On the Cauchy problem for Schrödinger–improved Boussinesq equations

2019 ◽  
Author(s):  
Tohru Ozawa ◽  
Kimitoshi Tsutaya
Keyword(s):  
Cauchy Problem ◽  
Boussinesq Equations ◽  
The Cauchy Problem

scholarly journals On the Existence of Long-Time Classical Solutions for the 2D Inviscid Boussinesq Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jiafa Xu ◽  
Lishan Liu
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Life Span ◽  
Boussinesq Equations ◽  
Classical Solutions ◽  
Buoyancy Frequency ◽  
General Initial Data ◽  
The Cauchy Problem ◽  
Long Time

In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with N being the buoyancy frequency. It is proved that for general initial data u 0 ∈ H s with s > 3 , the life span of the classical solutions satisfies T > C ln     N 3 / 4 .

On the Cauchy problems for certain Boussinesq-α equations

2010 ◽  
Vol 140 (2) ◽  
pp. 319-327 ◽  
Author(s):  
Yong Zhou ◽  
Jishan Fan
Keyword(s):  
Cauchy Problem ◽  
Smooth Solution ◽  
Boussinesq Equations ◽  
Regularity Criterion ◽  
Boussinesq System ◽  
Cauchy Problems ◽  
The Cauchy Problem ◽  
Boussinesq Systems

We study the Cauchy problem of certain Boussinesq-α equations in n dimensions with n = 2 or 3. We establish regularity for the solution under ▽u ∈ L1 (0, T; Ḃ0∞,∞(ℝn)). As a corollary, the smooth solution of the Leray-α–Boussinesq system exists globally, when n = 2. For the Lagrangian averaged Boussinesq equations, a regularity criterion ▽θ ∈ L1(0, T;L∞(ℝ2)) is established. Other Boussinesq systems with partial viscosity are also discussed in the paper.

scholarly journals The Well Posedness for Nonhomogeneous Boussinesq Equations

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2110
Author(s):  
Yan Liu ◽  
Baiping Ouyang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Positive Constant ◽  
Besov Spaces ◽  
Initial Velocity ◽  
Initial Temperature ◽  
Boussinesq Equations ◽  
Well Posedness ◽  
The Cauchy Problem ◽  
Critical Besov Spaces

This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces (θ,u)∈LT∞(B˙p,1N/p)×LT∞(B˙p,1N/p−1)⋂LT1(B˙p,1N/p+1) with 1<p<2N. We proved the global existence of the solution when the initial velocity is small with respect to the viscosity, as well as the initial temperature approaches a positive constant. Furthermore, we proved the uniqueness for 1<p≤N. Our results can been seen as a version of symmetry in Besov space for the Boussinesq equations.

scholarly journals Global well-posedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiaoqiang Dai ◽  
Shaohua Chen
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Control Problem ◽  
Boussinesq Equations ◽  
Global Dynamics ◽  
Blowup Solution ◽  
The Cauchy Problem ◽  
Generalized Boussinesq Equation ◽  
The Relationship ◽  
Time Blowup

<p style='text-indent:20px;'>The Cauchy problem of one dimensional generalized Boussinesq equation is treated by the approach of variational method in order to realize the control aim, which is the control problem reflecting the relationship between initial data and global dynamics of solution. For a class of more general nonlinearities we classify the initial data for the global solution and finite time blowup solution. The results generalize some existing conclusions related this problem.</p>

scholarly journals The Cauchy problem and decay rates for strong solutions of a Boussinesq system

2005 ◽  
Vol 2005 (7) ◽  
pp. 757-766 ◽  
Author(s):  
Francisco Guillén González ◽  
Márcio Santos da Rocha ◽  
Marko Rojas Medar
Keyword(s):  
Heat Transfer ◽  
Cauchy Problem ◽  
Viscous Fluid ◽  
Strong Solutions ◽  
Boussinesq Equations ◽  
Decay Rates ◽  
Boussinesq System ◽  
Three Dimension ◽  
The Cauchy Problem ◽  
Derivatives Of

The Boussinesq equations describe the motion of an incompressible viscous fluid subject to convective heat transfer. Decay rates of derivatives of solutions of the three-dimension-al Cauchy problem for a Boussinesq system are studied in this work.

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