an:07179075
Zbl 1435.35317
Ye, Zhuan
On the global well-posedness of one-dimensional fluid models with nonlocal velocity
EN
Pac. J. Math. 304, No. 2, 713-752 (2020).
00447834
2020
j
35Q35 76D03 35B60 35B65 35B44 44A15 35Q86 76U60
fluid model; nonlocal velocity; global-in-time solutions
A one-dimensional fluid flow model \(w_t+(1-\partial_{xx})^{-\beta}w w_x+\delta ((1-\partial_{xx})^{-\beta}w)_x +\nu (-\partial_{xx})^\gamma w=0\) includes as particular examples the (fractional) Burgers equation and the Camassa-Holm equations. The author studies local- and global-in-time solvability of this equation as well as blow-up criteria. Similar results are also obtained for a related equation involving the Hilbert transform as is in the dissipative surface quasigeostrophic model.
Piotr Biler (Wroc??aw)