This proceedings volume gathers a selection of outstanding papers presented at the International Conference: Toward World Consensus on Vortex Definition and Prediction (Vortex 2025) held on 13-16 December 2025 in Arlington, Texas, the USA.

Liutex is now in its seventh year since Dr. Chaoqun Liu first proposed it in 2018. During this period, much has changed. Researchers’ attitudes have shifted from skepticism and opposition to acceptance and support. Initially, the community focused on whether Liutex was correctly defined; scholars scrutinized it from every angle and approached it with cautious skepticism. Today, Liutex is widely regarded as a unique and accurate mathematical definition of a vortex and has been applied across a broad spectrum of disciplines.

It was against this backdrop that the International Conference: Toward World Consensus on Vortex Definition and Prediction was held. We are delighted that, as reported at the conference, Liutex has already been employed in studies ranging from hydrodynamics and tropical cyclones to magnetosheath turbulence, large-eddy simulation, gas–solid flows, supersonic tip vortices, and ice-covered channel flows. Since Liutex is the definition of vortex and vortex is involved in many areas, Liutex holds great promise for future applications.

This volume presents a selection of outstanding papers from the conference. It will provide graduate students, researchers and professionals in related fields with valuable insights and inspiration.

Dr. Chaoqun Liu is a Distinguished Professor at the Department of Mathematics, the University of Texas at Arlington, Texas, the USA.

Dr. Yiqian Wang is an Associate Professor at the School of Mathematical Science, Soochow University, China.

Dr. Yifei Yu is an Assistant Professor of Research at the Department of Mathematics, the University of Texas at Arlington, Texas, the USA.