 Global existence for the energy-subcritical generalized KdV equation

ID: global-existence-for-the-energy-subcritical-generalized-kdv-equation

For

p < 5

∥ u ∥_{p + 1}^{p + 1} ≲ ∥ u_{x} ∥_{2}^{(p - 1) /2} ∥ u ∥_{2}^{(p + 3) /2} .

The exponent of

∥ u_{x} ∥_{2}

is below two, so the conserved mass and energy control the

H^{1}

norm. The blowup alternative then extends every local

H^{1}

solution globally.

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