2 problems

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Bourgain's $X_{0,1/2}$ embedding conjecture
Let $X_{s,b}$ denote the Bourgain space associated with the KdV dispersion relation, consisting of distributions whose space-time Fourier transform is weighted by…
Conjectureopenbourgain-spaces kdv strichartz-estimatesarXiv posted 2 days ago
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Chen–Xiao's endpoint local well-posedness conjecture for the Benjamin equation
Chen–Xiao's conjecture. The initial value problem $$ is locally well-posed for $s=-3/4$ .
Conjectureopenbenjamin-equation bourgain-spaces well-posednessarXiv posted 2 days ago

Bourgain's X0,1/2X_{0,1/2}X0,1/2​ embedding conjecture