Quasi-Geostrophic Type Equations with Weak Initial Data
| dc.contributor.author | Wu, Jiahong | |
| dc.date.accessioned | 2019-03-25T22:27:36Z | |
| dc.date.available | 2019-03-25T22:27:36Z | |
| dc.date.issued | 1998-06-12 | |
| dc.description.abstract | We study the initial value problem for the quasi-geostrophic type equations ∂θ/∂t + u · ∇θ + (-Δ)λθ = 0, on ℝn x (0, ∞), θ(x, 0) = θ0(x), x ∈ ℝn, where λ(0 ≤ λ ≤ 1) is a fixed parameter and u = (uj) is divergence free and determined from θ through the Riesz transform uj = ±Rπ(j)θ, with π(j) a permutation of 1,2, ···, n. The initial data θ0 is taken in the Sobolev space Ĺr,p with negative indices. We prove local well-posedness when 1/2 < λ ≤ 1, 1 < p < ∞, n/p ≤ 2λ - 1, r = n/p - (2λ - 1) ≤ 0. We also prove that the solution is global if θ<sub>0</sub> is sufficiently small. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Wu, J. (1998). Quasi-geostrophic type equations with weak initial data. <i>Electronic Journal of Differential Equations, 1998</i>(16), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/7949 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 1998, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Quasi-geostrophic equations | |
| dc.subject | Weak data | |
| dc.subject | Well-posedness | |
| dc.title | Quasi-Geostrophic Type Equations with Weak Initial Data | |
| dc.type | Article |