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.
Bringmann,Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlin- earity II: dynamics, 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.
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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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.
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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.