On The Cauchy Problem for A 1D Euler-Alignment System in Besov Spaces  

作　　者：Yaojun Yang Yaojun Yang(College of Mathematics Science, Chongqing Normal University, Chongqing, China)

机构地区：[1]College of Mathematics Science, Chongqing Normal University, Chongqing, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第2期603-631,共29页应用数学与应用物理（英文）

摘　　要：In this paper, we investigate a 1D pressureless Euler-alignment system with a non-local alignment term, describing a kind of self-organizing problem for flocking. As a result, by the transport equation theory and Lagrange coordinate transformation, the local well-posedness of the solutions for the 1D pressureless Euler-alignment in Besov spaces  with 1≤p∞ is established. Next, the ill-posedness of the solutions for this model in Besov spaces  with 1≤p and  is also deduced. Finally, the precise blow-up criteria of the solutions for this system is presented in Besov spaces  with 1≤p .In this paper, we investigate a 1D pressureless Euler-alignment system with a non-local alignment term, describing a kind of self-organizing problem for flocking. As a result, by the transport equation theory and Lagrange coordinate transformation, the local well-posedness of the solutions for the 1D pressureless Euler-alignment in Besov spaces  with 1≤p∞ is established. Next, the ill-posedness of the solutions for this model in Besov spaces  with 1≤p and  is also deduced. Finally, the precise blow-up criteria of the solutions for this system is presented in Besov spaces  with 1≤p .

关 键 词：Euler-Alignment Equations Local Well-Posedness Blow-Up Criteria ILL-POSEDNESS 

分 类 号：O17[理学—数学]