A para-differential renormalization technique for nonlinear dispersive equations
Herr, Sebastian · Ionescu, Alexandru D. · Kenig, Carlos E. · Koch, Herbert
Original · EN
For α∈ (1,2) we prove that the initial-value problem ∂ₜ u+Dα∂ₓ u+∂ₓ(u²/2)=0 on Rₓₜ; u(0)=ϕ, is globally well-posed in the space of real-valued L²-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.
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