Weak solution of the merged mathematical equations of the polluted atmosphere |
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Authors: | Donatella Donatelli Nóra Juhász |
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Institution: | Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, L'Aquila, Italy |
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Abstract: | Considered as a geophysical fluid, the polluted atmosphere shares the shallow domain characteristics with other natural large-scale fluids such as seas and oceans. This means that its domain is excessively greater horizontally than in the vertical dimension, leading to the classic hydrostatic approximation of the Navier–Stokes equations. In the past there has been proved a convergence theorem for this model with respect to the ocean, without considering pollution effects. The novelty of this present work is to provide a generalization of their result translated to the atmosphere, extending the fluid velocity equations with an additional convection–diffusion equation representing pollutants in the atmosphere. |
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Keywords: | compactness hydrostatic approximation Navier–Stokes equations pollution evolution equation shallow domains weak solutions |
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