The study of free boundary problems in the Navier-Stokes equations addresses the subtle interplay between the dynamics of viscous, incompressible fluids and the evolution of interfaces whose locations ...

The compressible Navier-Stokes equations remain a cornerstone in the study of fluid dynamics, encapsulating the evolution of fluids whose density variations are significant. Recent advancements have ...

Although Navier–Stokes equations are the foundation of modern hydrodynamics, adapting them to quantum systems has so far been ...

In a 2001 paper, S. Montgomery-Smith provides a one-dimensional model for the three-dimensional, incompressible Navier-Stokes equations, for which he proves the blow-up of solutions associated with a ...

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations. For nearly two centuries, all kinds of researchers ...

The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous features of the physical world: the flow of fluids. The equations, which date to the 1820s, are today used to ...

Partial differential equations can describe everything from planetary motion to plate tectonics, but they’re notoriously hard to solve. Ms Tech | Science Photo Library via AP Unless you’re a physicist ...

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Equations are the bedrock of science, expressing how numbers or physical properties relate at a fundamental level. Without equations, most of our technology would never have been invented. We may have ...