The global regularity problem for the Navier-Stokes
Research gap analysis derived from 3 mathematics papers in our local library.
The gap
The global regularity problem for the Navier-Stokes equations has been open for over two centuries, - The Lagrangian approach provides a new perspective on the Navier-Stokes equations
Evidence profile
Sourced from the stated research gap and future-work section of the source papers, classified as general, spanning 2 journals.
Research trend
Established — well-defined area with open sub-problems.
Supporting evidence — 4 representative gaps
- ...this (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi
The global regularity problem for the Navier-Stokes equations has been open for over two centuries, - The Lagrangian approach provides a new perspective on the Navier-Stokes equations
generalstated research gapevidence 5/5Keywords: global regularity problem navier-stokes equations has been open - GLOBAL REGULARITY OF THE THREE-DIMENSIONAL NAVIER–STOKES EQUATIONS VIA LOCALIZED COUPLING ALGEBRA AND BRANCH EXHAUSTION (2026) · Zenodo (CERN European Organization for Nuclear Research) · doi
The global regularity problem for the three-dimensional Navier-Stokes equations is a long-standing open problem in mathematics. Prior work has not fully resolved the problem. The paper identifies a gap in the existing literature and introduces a new approach to address it.
generalstated research gapevidence 5/5Keywords: global regularity problem three-dimensional navier-stokes equations long-standing open - The One-Dimensional Compressible Navier–Stokes Equations in Critical Regularity Spaces (2026) · SIAM Journal on Mathematical Analysis · doi
The one-dimensional case of the compressible Navier-Stokes equations has not been previously studied in critical regularity spaces. The existing literature has a gap in the analysis of the equations in this context. The authors aim to fill this gap by establishing the global well-posedness and optimal time decay estimates for the equations.
generalstated research gapevidence 5/5Keywords: one-dimensional case compressible navier-stokes equations has been previously - The One-Dimensional Compressible Navier–Stokes Equations in Critical Regularity Spaces (2026) · SIAM Journal on Mathematical Analysis · doi
Future studies could extend the results to the multidimensional case or more general initial data. The authors suggest that further research could be conducted on the analysis of the compressible Navier-Stokes equations using the mass Lagrangian coordinates system. The study could be generalized to other types of fluid dynamics equations.
generalfuture-work sectionevidence 5/5Keywords: future studies extend results multidimensional case general initial
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