scholarly journals The Cauchy problem for a generalized $b$-equation with higher-order nonlinearities in critical Besov spaces and weighted $L^p$ spaces

2014 ◽  
Vol 34 (11) ◽  
pp. 4967-4986 ◽  
Author(s):  
Shouming Zhou
Keyword(s):  
Cauchy Problem ◽  
Besov Spaces ◽  
Higher Order ◽  
The Cauchy Problem ◽  
Critical Besov Spaces

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 The Cauchy Problem for Higher-Order KP Equations

1999 ◽  
Vol 153 (1) ◽  
pp. 196-222 ◽  
Author(s):  
J.C. Saut ◽  
N. Tzvetkov
Keyword(s):  
Cauchy Problem ◽  
Higher Order ◽  
The Cauchy Problem ◽  
Kp Equations

scholarly journals The Cauchy problem for higher-order modified Camassa–Holm equations on the circle

2019 ◽  
Vol 187 ◽  
pp. 397-433 ◽  
Author(s):  
Wei Yan ◽  
Yongsheng Li ◽  
Xiaoping Zhai ◽  
Yimin Zhang
Keyword(s):  
Cauchy Problem ◽  
Higher Order ◽  
The Cauchy Problem
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