Luis Caffarelli, Navier-Stokes existence and smoothness

[@shaikimamsab8926]

I am going to give the solution for above question with in 3 to 4 years . wish me good luck.

[@yagabharath6815]

May God bless you

[@yagabharath6815]

Good luck bro if you solve plz explain me I give my number

[@deepaksinghrawat5246]

Good luck...

[@giovannipini7625]

how is it going?

[@hrkalita159]

bro any advancement

[@jhanolaer8286]

If we advect the scalar it can cause of diffusion, and if we advect the Vectors it can cause the collision.

[@rensleymeulens7273]

I indeed have to tell you that your comment of "no progress have been made on the problem" is incorrect. Please do refer at the "recently" [January 2022] found exact N-soliton solutions of the Navier-Stokes differential equations. The manuscript has been peer-reviewed and published by the prestigious American Institute of Physics and Witten by r. Meulens and cited as R. Meulens , "A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation", AIP Advances 12,

[@p3dr0s4]

@rensleymeulens7273, Did you found the singularity mentioned by Caffarelli?

[@rensleymeulens7273]

@@p3dr0s4 Hi thank you for your Question. A snapshot of what Prof.Caffarrelli said about "singularity": I will qoute with your permission:”the pressure (from infinity) squeeze the flow quite right to create a singularity”. Indeed the stream-line solutions of the viscous and incompressible Navier-Stokes differential equations are Hermite functions which are Euler-Cornu Spirals (swirls) in the complex plane and the infinitely many derivatives of the Error function. Thus all the solutions do contain singularities, called poles, orchestrated by the begin conditions through a Weierstrass p-function calculated out of the begin conditions (boundaries) themselves. As a matter of fact the solutions may be interpreted as moving boundaries. the pressure is then calculated with the following formula: pr = F/Area=m *a/Area =m*du/dt/Area, u is time evolutive main stream velocity is calculated in the document. There are different bifurcation points for the solutions depending on the scale, the flow begin velocity and Reynolds’s number of the problem. I recommend you to read the published paper for further details. The digital link to the document is doi.org/10.1063/5.0074083 Best wishes and thanks for your question. If you have more question please feel free to contact me.

[@jespervalgreen6461]

This lecture is from 2001

[@jasonandrewismail2029]

incorrect interpretation at 20 min to 22 min. the Lagrangian does not represent what he said,

[@justabarroth773]

Also the gradient is calculated by multiplying by the original exponent instead of dividing.

[@ArtSellerBluemehr]

Solutions to the incompressible and viscid Navier-Stokes differential equations has been found! And published by the American Institute of Physics. The author is rensley meulens. The manuscript is called R. Meulens , "A note on N-soliton solutions for the viscid incompressible Navier-Stokes differential equation", AIP Advances 12, 015308 (2022)