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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2026 2verdicts
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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.
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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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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.