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Bahouri, H., Chemin, J.-Y. and Danchin, R. (2011) Fourier Analysis and Nonlinear Partial Differential Equations. Springer Science & Business Media, 343.
https://doi.org/10.1007/978-3-642-16830-7

has been cited by the following article:

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

  AUTHORS: Yaojun Yang

  KEYWORDS: Euler-Alignment Equations, Local Well-Posedness, Blow-Up Criteria, Ill-Posedness

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.2, February 29, 2024

  ABSTRACT: 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 .