Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces

We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from u 0 are discontinuous at t = 0.

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Veröffentlicht in:	Applications of Mathematics 2024-12, Vol.69 (6), p.757-767
Hauptverfasser:	Yu, Yanghai, Liu, Fang
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Applications of Mathematics Classical and Continuum Physics Euler-Lagrange equation Fluid flow Function space Ill posed problems Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Navier-Stokes equations Optimization Theoretical
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Beschreibung
Zusammenfassung:	We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from u 0 are discontinuous at t = 0.
ISSN:	0862-7940 1572-9109
DOI:	10.21136/AM.2024.0089-24