On waveguides, the shell-type Strichartz estimate is global and derivative-free on R2×T but must lose derivatives on R×T2, yielding first local well-posedness for the partially periodic Zakharov system.
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On restricted-type Strichartz estimates and the applications
On waveguides, the shell-type Strichartz estimate is global and derivative-free on R2×T but must lose derivatives on R×T2, yielding first local well-posedness for the partially periodic Zakharov system.