New function spaces reformulate ell^q L^p decoupling inequalities for sphere and light cone, are invariant under half-wave propagators, and improve fractional integration and local smoothing estimates.
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New local smoothing estimates via ℓ²-decoupling yield improved well-posedness for the 2D cubic nonlinear wave equation with slowly decaying data.
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Function spaces for decoupling
New function spaces reformulate ell^q L^p decoupling inequalities for sphere and light cone, are invariant under half-wave propagators, and improve fractional integration and local smoothing estimates.
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Nonlinear wave equations with slowly decaying initial data
New local smoothing estimates via ℓ²-decoupling yield improved well-posedness for the 2D cubic nonlinear wave equation with slowly decaying data.