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

Jun Wang; Zhaoyang Yin

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arXiv · 2512.11491

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

Jun Wang·Zhaoyang Yin

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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.

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Jun Wang, Zhaoyang Yin. 2025-12-12. Existence and dependency results for coupled Schr\"odinger equations with critical exponent on waveguide manifold. https://arxiv.org/abs/2512.11491

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