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This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation The main results show that regularity or polynomial decay of the data on the positive half-line yields regularity in the solution for positive times. [ABSTRACT FROM AUTHOR]

We consider the generalized Korteweg-de Vries (gKdV) equation with the time oscillating nonlinearity: Under the suitable assumption on g, we show that if the nonlinear term is mass critical or supercritical i.e., $${p \geq 5}$$ and $${u(0) \in \dot{H}^{s_{p}}}$$ , where $${s_{p} = 1/2 - 2/(p-1)}$$ is a scale critical exponent, then there exists a unique global solution to (gKdV) provided that $${|\omega|}$$ is sufficiently large. We also obtain the behavior of the solution to (gKdV) as $${|\omega| \to \infty}$$ . [ABSTRACT FROM AUTHOR]