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 3verdicts
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The paper defines enhanced probabilistic well-posedness by imposing stability at the origin and reinterprets recent 'beyond variance blowup' results for dispersive PDEs as probabilistic ill-posedness.
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.
citing papers explorer
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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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On probabilistic ill-posedness
The paper defines enhanced probabilistic well-posedness by imposing stability at the origin and reinterprets recent 'beyond variance blowup' results for dispersive PDEs as probabilistic ill-posedness.
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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.