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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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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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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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.