Complex analytic solutions for the TQG model

TL;DR

This paper establishes conditions for the TQG model to have solutions that are complex analytic in time, extending previous work on Euler equations to a geophysical fluid dynamics context.

Contribution

It introduces a novel condition ensuring complex analyticity of solutions for the TQG model, expanding the mathematical understanding of its solution space.

Findings

Identifies conditions for holomorphic solutions in time for TQG

Extends previous Euler equation results to TQG model

Provides a framework for complex analytic solutions in geophysical fluid dynamics

Abstract

We present a condition under which the thermal quasi-geostrophic (TQG) model possesses a solution that is holomorphic in time with values in the Gevrey space of complex analytic functions. This can be seen as the complex extension of the work by Levermore and Oliver (1997) for the generalized Euler equation but applied to the TQG model.