@article{Zhang2025, 
author = {Yuanyuan Zhang},
title = {Non-uniform dependence for the inviscid Boussinesq equations in Besov spaces},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {25624-25638},
keywords = {Boussinesq equations, Cauchy problem, non-uniform continuous dependence, Besov spaces, approximate solutions},
url = {https://www.sciopen.com/article/10.3934/math.20251135},
doi = {10.3934/math.20251135},
abstract = {This paper addresses the initial value problem to the inviscid Boussinesq equations in              R        2  . We rigorously show that the data-to-solution map fails to be uniformly continuous within a broad class of nonhomogeneous Besov spaces        B          p      ,      r        s    (            R        2    ) cited in [20] (i.e.,    s  >  1  +      2    p    ,  1  <  p  <  ∞  ,  1  ≤  r  ≤  ∞ or    s  =  1  +      2    p    ,  1  <  p  <  ∞  ,  r  =  1). This result partially extends the nowhere uniform continuity previously demonstrated by Inci[9] in the Sobolev spaces        H    m    (            R        2    ) with    m  >  2. Our proof leverages the interaction between terms of low and high frequencies. Besides, the linearized system to the inviscid Boussinesq equations plays a pivotal role in the construction of appropriate approximate solutions.}
}