Mathematical Analysis of Navier-Stokes Equations for Incompressible Liquids

@article{Ladyzhenskaya1975MathematicalAO,
  title={Mathematical Analysis of Navier-Stokes Equations for Incompressible Liquids},
  author={O. Ladyzhenskaya},
  journal={Annual Review of Fluid Mechanics},
  year={1975},
  volume={7},
  pages={249-272}
}
Let viscous incompressible liquid occupy a volume ~ of three-dimensional Euclidean space E3. Introducing a Cartesian orthogonal frame xl, x2, x3 in E3, we denote a point (xl, x2, x3) by x. Let us denote the velocity and pressure of the liquid at the point x and at the instant t by v(x, t) and p(x, t), respectively, v~(x, t), i-1, 2, 3, being the projections of the velocity on axes x~. The scale may be chosen in such a way that the density is equal to unity. Then according to the Navier-Stokes… Expand
54 Citations
Hydrodynamics at the smallest scales: a solvability criterion for Navier–Stokes equations in high dimensions
Hydrodynamics at the smallest scales: a solvability criterion for Navier–Stokes equations in high dimensions
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