Existence and dependency results for coupled Schr\"odinger equations with critical exponent on waveguide manifold

Jun Wang; Zhaoyang Yin

Existence and dependency results for coupled Schr\"odinger equations with critical exponent on waveguide manifold

Analysis of PDEs 2025-12-15 v1

Authors: Jun Wang , Zhaoyang Yin

Abstract

We study the coupled Schr\"odinger equations with critical exponent on $\mathbb{R}^3 \times \mathbb{T}$ . With the help of scaling argument and semivirial-vanishing technology, we obtain the existence and $y$ -dependence of solution, the tori can be generalized to $1$ -dimensional compact Riemannian manifold. Moreover, the conclusion of this paper can be extended to systems with any number of components.

Keywords

Schr\"odinger equations critical exponent existence dependency waveguide manifold scaling argument semivirial-vanishing

Cite

@article{arxiv.2512.11491,
  title  = {Existence and dependency results for coupled Schr\"odinger equations with critical exponent on waveguide manifold},
  author = {Jun Wang and Zhaoyang Yin},
  journal= {arXiv preprint arXiv:2512.11491},
  year   = {2025}
}

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22pages

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