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dc.contributor.authorGala, Sadek ( )
dc.identifier.citationGala, S. (2005). Quasi-geostrophic equations with initial data in Banach spaces of local measures. Electronic Journal of Differential Equations, 2005(63), pp. 1-22.en_US

This paper studies the well posedness of the initial value problem for the quasi-geostrophic type equations

tθ + u∇θ + (-∆)γ θ = 0 on ℝd x]0, +∞[
θ(x, 0) = θ0(x), x ∈ ℝd

where 0 < γ ≤ 1 is a fixed parameter and the velocity field u = (u1, u2,...,ud is divergence free; i.e., ∇u = 0). The initial data θ0 is taken in Banach spaces of local measures (see text for the definition), such as Multipliers, Lorentz and Morrey-Campanato spaces. We will focus on the subcritical case 1/2 < γ ≤ 1 and we analyse the well-posedness of the system in three basic spaces: Ld/r,∞, Ẋr and Mp,d/r, when the solution is global for sufficiently small initial data. Furthermore, we prove that the solution is actually smooth. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.

dc.format.extent23 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectQuasi-geostrophic equationen_US
dc.subjectLocal spacesen_US
dc.subjectMild solutionsen_US
dc.subjectSelf-similar solutionsen_US
dc.titleQuasi-geostrophic equations with initial data in Banach spaces of local measuresen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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