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- W4387168061 abstract "We consider the initial value problem (IVP) associated to a quadratic Schrodinger system begin{equation*} begin{cases} i partial_{t} v pm Delta_{g} v - v = epsilon_{1} u bar{v}, & t in mathbb{R},; x in M, [2ex] i sigma partial_{t} u pm Delta_{g} u - alpha u = frac{epsilon_{2}}{2} v^{2}, & sigma > 0, ;alpha in mathbb{R},; epsilon_{i} in mathbb{C}, (i = 1, 2),[2ex] (v(0), u(0)) = (v_0, u_0), end{cases} end{equation*} posed on a $d$-dimensional sphere $ mathbb{S}^{d}$ or a compact Zoll manifold $M$. Considering $sigma=frac{theta}{beta}$ with $theta, betain {n^2:ninmathbb{Z}}$ we derive a bilinear Strichartz type estimate and use it to prove the local well-posedness results for given data $(v_0, u_0)in H^s(M)times H^s(M)$ whenever $s>frac{1}{4}$ in the case $M = mathbb{S}^{2}$ or a Zoll manifold, and $s > frac{d - 2}{2}$ in the case $M = mathbb{S}^{d}$ ($d geq 3$) induced with the canonical metric. Moreover, in dimensions $2$ and $3$, we use a Gagliardo-Nirenberg type inequality to prove that the local solution can be extended globally in time whenever $s geq 1$." @default.
- W4387168061 created "2023-09-30" @default.
- W4387168061 creator A5008853066 @default.
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- W4387168061 date "2019-06-07" @default.
- W4387168061 modified "2023-09-30" @default.
- W4387168061 title "Local and global well-posedness for a quadratic Schrodinger system on spheres and Zoll manifolds" @default.
- W4387168061 doi "https://doi.org/10.48550/arxiv.1906.03245" @default.
- W4387168061 hasPublicationYear "2019" @default.
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