A physical-space bilinear estimate method reproduces the sharpest known local well-posedness thresholds for the 2d and 3d Zakharov system without Bourgain spaces.
Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations
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abstract
We give a simpler proof for the local well-posedness of the modified Korteweg-de Vries equations and modified Benjamin-Ono equation in $H^{\frac{1}{4}}(\mathbb{R})$ and $H^{\frac{1}{2}}(\mathbb{R})$, respectively. The proof is based on the Strichartz estimate, dyadic decomposition and a bilinear estimate given by a new type of div-curl lemma.
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Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations (II)
A physical-space bilinear estimate method reproduces the sharpest known local well-posedness thresholds for the 2d and 3d Zakharov system without Bourgain spaces.