Pathwise local well-posedness of stochastic nonlinear wave equations with multiplicative noise is established in optimal regularity ranges by unifying Fourier restriction norm methods with rough path integration.
Gubinelli,Controlling rough paths, J
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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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Fourier restriction norm method adapted to controlled paths: stochastic wave equations
Pathwise local well-posedness of stochastic nonlinear wave equations with multiplicative noise is established in optimal regularity ranges by unifying Fourier restriction norm methods with rough path integration.
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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.