Nonlinear Stability and Advanced Numerical Methods in Fluid and Hamiltonian Systems

Dear Colleagues,

Fluid and Hamiltonian systems are fundamental to understanding a vast array of natural phenomena and engineering applications, from geophysical flows and plasma confinement to micro-scale transport and the design of advanced materials. The intricate nonlinear dynamics and stability behaviors inherent in these systems present enduring theoretical and computational challenges. This Special Issue, titled “Nonlinear Stability and Advanced Numerical Methods in Fluid and Hamiltonian Systems” aims to collate cutting-edge research that addresses these challenges.

The scope of this issue encompasses both fundamental theoretical advances and innovative numerical methodologies. We seek contributions that explore nonlinear instability mechanisms, transition to turbulence, long-time dynamics, and the interplay among structure, stability, and dissipation. A key focus is the development and application of advanced numerical algorithms—including high-fidelity simulations, structure-preserving schemes, and multi-scale modeling—capable of accurately capturing the complex behavior of these systems.

By bringing together diverse perspectives, this issue will provide a platform that fosters new insights and bridges the gap between mathematical theory, computational science, and practical application. It will serve as a valuable resource, supplementing the existing literature by highlighting emerging trends and state-of-the-art solutions in the analysis and computation of complex nonlinear systems.

Dr. Zhaodong Ding
Prof. Dr. Andrea Giacobbe
Guest Editors

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