Landau-Lifshitz Navier-Stokes equation on which page of the textbook?

In summary, the conversation revolves around the search for the Landau-Lifshitz Navier-Stokes (LLNS) equation in the Landau-Lifshitz Fluid Mechanics book. While some papers mention it, the exact page in the book is not specified. It is suggested that the equation may have been removed from the second edition of the book or moved to another volume.
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I see some papers mentioning the fluctuating hydrodynamics, which originates from the Landau-Lifshitz Navier-Stokes (LLNS) equation. I know that the LLNS equation has added a thermal fluctuation term to the N-S equation, but I still couldn't find it on the Landau-Lifshitz Fluid Mechanics book. The references of those papers just say it is in the Landau-Lifshitz book, without telling me exactly which page it is on. Anyone know this?

Thanks.
 
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  • #2
I am encountering exactly the same issue. Where you able to find the equation on the textbook?
Thank you.
 
  • #3
I have the same problem.
I would really appreciate if anyone can tell me where to find the LLNS equation on the book.
 
  • #4
Is it equation 1 here?
 
  • #5
It may depend on which edition of the book you have handy. The first edition has an entire unit at the end titled "XVII. Fluctuations in Fluid Mechanics" which has been removed in the second edition. It's possible that these two chapters were moved to another volume (e.g. volume 5, statistical physics) but I am not really sure since I am not familiar with that book or with anything other than the 2nd edition of volume 6.
 
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1. What is the Landau-Lifshitz Navier-Stokes equation?

The Landau-Lifshitz Navier-Stokes equation is a mathematical model used to describe the motion of a fluid in a given space. It combines the Navier-Stokes equation, which describes the movement of a viscous fluid, with the Landau-Lifshitz equation, which takes into account the effects of magnetic fields on the fluid.

2. What is the significance of the Landau-Lifshitz Navier-Stokes equation?

The Landau-Lifshitz Navier-Stokes equation is significant because it allows for the study of fluid motion in the presence of magnetic fields, which is important in many fields such as plasma physics, astrophysics, and materials science. It also provides insight into the behavior of complex fluids, such as those with magnetic particles suspended in them.

3. How is the Landau-Lifshitz Navier-Stokes equation derived?

The Landau-Lifshitz Navier-Stokes equation is derived from the Navier-Stokes equation and the Landau-Lifshitz equation, by combining the two equations and incorporating the effects of magnetic fields on the fluid. The resulting equation is a non-linear partial differential equation that describes the motion of a fluid in the presence of magnetic fields.

4. What are the assumptions made in the Landau-Lifshitz Navier-Stokes equation?

The Landau-Lifshitz Navier-Stokes equation assumes that the fluid being studied is incompressible, has a constant density, and is subject to a uniform magnetic field. It also assumes that the fluid is viscous and that the magnetic field does not change with time.

5. What are some applications of the Landau-Lifshitz Navier-Stokes equation?

The Landau-Lifshitz Navier-Stokes equation has applications in many fields, including plasma physics, astrophysics, and materials science. It is used to study the behavior of complex fluids, such as ferrofluids and liquid crystals, and to model the flow of fluids in the presence of magnetic fields, such as in magnetic levitation systems and magnetic drug targeting. It is also used in the study of geophysical phenomena, such as the Earth's magnetic field and the flow of fluids in the Earth's core.

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