scholarly journals Global existence and nonexistence of solution for Cauchy problem of two-dimensional generalized Boussinesq equations

2015 ◽  
Vol 422 (2) ◽  
pp. 1116-1130 ◽  
Author(s):  
Hongwei Zhang ◽  
Qingying Hu
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Boussinesq Equations ◽  
Two Dimensional ◽  
Existence And Nonexistence

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.

Global Existence of Solution for Cauchy Problem of Two-Dimensional Boussinesq-Type Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Qingying Hu ◽  
Chenxia Zhang ◽  
Hongwei Zhang
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Initial Data ◽  
Global Existence ◽  
Exponential Growth ◽  
Type Equation ◽  
Global Weak Solution ◽  
Existence Of Solution ◽  
Two Dimensional ◽  
The Cauchy Problem

In this paper, we consider the Cauchy problem of two-dimensional Boussinesq-type equations utt-Δu-Δutt+Δ2u=Δfu. Under the assumptions that fu is a function with exponential growth at infinity and under some assumptions on the initial data, we prove the existence of global weak solution.

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