Weak solution of the merged mathematical equations of the polluted atmosphere. (13th July 2020)

• Record Type: Journal Article
• Authors: Donatelli, Donatella; Juhász, Nóra
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 15(2020)
• Page Start: 9245
• Page End: 9261
• Publication Date: 2020-07-13
• Subjects: compactness -- hydrostatic approximation -- Navier–Stokes equations -- pollution evolution equation -- shallow domains -- weak solutions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6618
• Languages: English
• ISSNs: 0170-4214

Abstract

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.