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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Proves local well-posedness of the extended Schrödinger-Benjamin-Ono system in H^{s+1/2}(R) × H^s(R) for s ≥ 0 and global well-posedness in the energy space with small L² data on the Schrödinger component.
Local well-posedness holds for the Schrödinger-ILW system in H^{s+1/2}(R) × H^s(R) for all s ≥ 0 (global at s = 1/2) when |ν| ≠ 1, via energy estimates, Bourgain spaces and Tao gauge.
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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.
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Local and global well-posedness for the extended Schr\"{o}dinger-Benjamin-Ono system
Proves local well-posedness of the extended Schrödinger-Benjamin-Ono system in H^{s+1/2}(R) × H^s(R) for s ≥ 0 and global well-posedness in the energy space with small L² data on the Schrödinger component.
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Well-Posedness of the Schr\"odinger -- Intermediate Long Wave system
Local well-posedness holds for the Schrödinger-ILW system in H^{s+1/2}(R) × H^s(R) for all s ≥ 0 (global at s = 1/2) when |ν| ≠ 1, via energy estimates, Bourgain spaces and Tao gauge.