Irregular modulation of dispersion yields pathwise regularization-by-noise for multiplicative Young noise on stochastic KdV, giving local well-posedness in every Hs.
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2026 2verdicts
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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.
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Nonlinear PDEs with modulated dispersion III: multiplicative noises
Irregular modulation of dispersion yields pathwise regularization-by-noise for multiplicative Young noise on stochastic KdV, giving local well-posedness in every Hs.
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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.