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 form the cornerstone of fluid dynamics, describing the motion of viscous compressible fluids under conservation of mass, momentum and energy. By incorporating ...

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 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 ...

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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 ...

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 ...

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 ...