Well-posedness for the fifth-order KdV equation in the energy space

By Carlos E. Kenig, Didier Pilod. 2012

59 citations recorded by the source corpus.

We prove that the initial value problem (IVP) associated to the fifth order KdV equation {equation} \label{05KdV} \partial_tu-\alpha\partial^5_x u=c_1\partial_xu\partial_x^2u+c_2\partial_x(u\partial_x^2u)+c_3\partial_x(u^3), {equation} where $x \in \mathbb R$, $t \in \mathbb R$, $u=u(x,t)$ is a real-valued function and $\alpha, \ c_1, \ c_2, \ c_3$ are real constants with $\alpha \neq 0$, is locally well-posed in $H^s(\mathbb R)$ for $s \ge 2$. In the Hamiltonian case (\textit i.e. when $c_1=c_2$), the IVP associated to \eqref{05KdV} is then globally well-posed in the energy space $H^2(\mathbb R)$.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/26605e8008a38a7e46839c56715c55590818e0e3

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In Mathematical Physics

  1. Rowan Killip
  2. Monica Visan
  3. B. Dodson
  4. Aynur Bulut
  5. Vedran Sohinger
  6. Terence Tao
  7. Xiaoyi Zhang
  8. Barry Simon

In Statistical and Nonlinear Physics

  1. Rowan Killip
  2. Monica Visan
  3. Barry Simon
  4. B. Dodson

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