Global well-posedness and optimal pathwise unconditional uniqueness for the additive-noise stochastic KdV on R in L² are established by adapting the Fourier restriction norm method to Fourier-Lebesgue spaces in time.
Bourgain,Fourier transform restriction phenomena for certain lattice subsets and applications to non- linear evolution equations
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Unconditional well-posedness of the stochastic Korteweg-de Vries equation on the real line
Global well-posedness and optimal pathwise unconditional uniqueness for the additive-noise stochastic KdV on R in L² are established by adapting the Fourier restriction norm method to Fourier-Lebesgue spaces in time.