Sharp Shell-Type Bilinear Decoupling and Improved Strichartz Estimates on Tori

@misc{wang2026sharp,
  title = {{Sharp Shell-Type Bilinear Decoupling and Improved Strichartz Estimates on Tori}},
  author = {Jiajun Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.19531},
  eprint = {2608.19531},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.19531},
}

TY  - UNPB
TI  - Sharp Shell-Type Bilinear Decoupling and Improved Strichartz Estimates on Tori
AU  - Jiajun Wang
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2608.19531
UR  - https://arxiv.org/abs/2608.19531
AB  - We establish sharp bilinear decoupling under shell-type Fourier support restrictions and show that its optimal coefficient need not be optimal for the corresponding periodic bilinear Strichartz estimate. For N_1≥ N_2, the sharp decoupling coefficient is N_2^(2d−7)/4(1+N_2^2/N_1)^1/4, up to an N_2^ε loss. This yields a shell-type bilinear Strichartz estimate with the same coefficient on every fixed rectangular torus, including irrational tori. On the standard square torus, we improve this Strichartz estimate for d≥6, obtaining the optimal coefficient (N_2^d−4+N_2^d−2/N_1)^1/2, up to an N_2^ε loss. The proof combines localization in spatial frequency and energy, a circle-method estimate for the localized high-frequency factor, and a linear estimate on arbitrarily oriented strips. As applications, we obtain estimates for toral eigenfunctions, mixed additive energy, and separated nonlinear smoothing for the periodic Zakharov system.
ER  -