The wave breaking for Whitham-type equations revisited
arXiv:2006.03803 · doi:10.1137/20M1345207
Abstract
We prove wave breaking (shock formation) for some Whitham-type equations which include the Burgers-Hilbert equation, the fractional Korteweg-de Vries equation, and the classical Whitham equation. The result seems to be new for the Burgers-Hilbert equation. In the other cases we provide simpler proofs than the known ones.
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Cited by in corpus (11)
- Shock formation for the Burgers-Hilbert equation
- On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation
- Enhanced existence time of solutions to evolution equations of Whitham type
- Gradient blow-up for dispersive and dissipative perturbations of the Burgers equation
- Highest Cusped Waves for the Burgers-Hilbert equation
- Wave breaking for the generalized Fornberg-Whitham equation
- On the approximation of vorticity fronts by the Burgers-Hilbert equation
- Refined wave breaking for the generalized Fornberg-Whitham equation
- Stability of traveling waves for the Burgers-Hilbert equation
- Rigorous derivation of the Whitham equations from the water waves equations in the shallow water regime
- On the Cauchy problem of dispersive Burgers type equations