Enhanced existence time of solutions to evolution equations of Whitham type
arXiv:2008.12722 · doi:10.3934/dcds.2022035
Abstract
We show that Whitham type equations u_t + u u_x -L u_x = 0, where L is a general Fourier multiplier operator of order α\in [-1,1], α\neq 0, allow for small solutions to be extended beyond their expected existence time. The result is valid for a range of quadratic dispersive equations with inhomogeneous symbols in the dispersive range given by α, and should be extendable to other equations of the same relative dispersive strength.
References in corpus (9)
- Global well-posedness of the 3-D full water wave problem
- A numerical approach to Blow-up issues for dispersive perturbations of Burgers' equation
- On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
- On Whitham's conjecture of a highest cusped wave for a nonlocal dispersive equation
- Long-time existence for multi-dimensional periodic water waves
- The wave breaking for Whitham-type equations revisited
- Enhanced existence time of solutions to the fractional Korteweg-de Vries equation
- Solitary wave solutions to a class of modified Green-Naghdi systems
- Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity