Well-posedness and ill-posedness for the 3D generalized Navier-Stokes equations in $\dot{F}^{-\alpha,r}_{\frac{3}{\alpha-1}}$
Viscous Aubry-Mather theory and the Vlasov equation
February 2014, 34(2): 421-436. doi: 10.3934/dcds.2014.34.421
On the existence and asymptotic stability of solutions for unsteady mixing-layer models
Tómas Chacón-Rebollo 1, , Macarena Gómez-Mármol 1, and Samuele Rubino 1,
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Calle Tarfia, s/n, 41012, Sevilla, Spain, Spain, Spain
Received November 2012 Revised May 2013 Published August 2013
We introduce in this paper some elements for the mathematical analysis of turbulence models for oceanic surface mixing layers. We consider Richardson-number based vertical eddy diffusion models. We prove the existence of unsteady solutions if the initial condition is close to an equilibrium, via the inverse function theorem in Banach spaces. We use this result to prove the non-linear asymptotic stability of equilibrium solutions.
Keywords: inverse function theorem., Oceanic turbulent mixing-layer models, gradient Richardson number.
Mathematics Subject Classification: Primary: 35Q86, 37N10; Secondary: 76F4.
Citation: Tómas Chacón-Rebollo, Macarena Gómez-Mármol, Samuele Rubino. On the existence and asymptotic stability of solutions for unsteady mixing-layer models. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 421-436. doi: 10.3934/dcds.2014.34.421
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Tómas Chacón-Rebollo Macarena Gómez-Mármol Samuele Rubino