Approximate Deconvolution Model in a bounded domain with a vertical regularization

TL;DR

This paper proves the global existence of weak solutions for a three-dimensional Approximate Deconvolution Model with vertical filtering in a bounded cylindrical domain, using refined energy methods.

Contribution

It establishes the existence and uniqueness of global weak solutions for the model in a bounded domain, extending previous work with refined energy techniques.

Findings

Existence of a unique global weak solution

Refinement of energy methods for the model

Application to bounded cylindrical domains

Abstract

We study the global existence issue for a three-dimensional Approximate Deconvolution Model with a vertical filter. We consider this model in a bounded cylindrical domain where we construct a unique global weak solution. The proof is based on a refinement of the energy method given by Berselli in [3].