On the global well-posedness of one-dimensional fluid models with nonlocal velocity (Q2305510)
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| Language | Label | Description | Also known as |
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| English | On the global well-posedness of one-dimensional fluid models with nonlocal velocity |
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On the global well-posedness of one-dimensional fluid models with nonlocal velocity (English)
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11 March 2020
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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.
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fluid model
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nonlocal velocity
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global-in-time solutions
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