Long time dynamics of a fractional dissipative model of electroconvection in bounded domains

E. Abdo; M. Ignatova

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arXiv · 2309.17423

Long time dynamics of a fractional dissipative model of electroconvection in bounded domains

E. Abdo·M. Ignatova

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Abstract

We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-posedness, global regularity and long time dynamics of the model in bounded smooth domains with Dirichlet boundary conditions. We prove the existence and uniqueness of exponentially decaying in time solutions for $H^1$ initial data regardless of the fractional dissipative regularity. In the presence of time independent body forces in the fluid, we prove the existence of a compact finite dimensional global attractor. In the case of periodic boundary conditions, we prove that the unique smooth solution is globally analytic in time, and belongs to a Gevrey class of functions that depends on the dissipative regularity of the model.

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E. Abdo, M. Ignatova. 2023-09-29. Long time dynamics of a fractional dissipative model of electroconvection in bounded domains. https://arxiv.org/abs/2309.17423

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