Abstract
A solution to the 6thmillenium problem, respect to breakdown of Navier-Stokes solutions and the bounded energy. We have proved that there are initial velocities and forces such that there is no physically reasonable solution to the Navier-Stokes equations for, which corresponds to the case (C) of the problem relating to Navier-Stokes equations available on the website of the Clay Institute
Highlights
IntroductionA way I see to prove the breakdown solutions of Navier-Stokes equations, following the described in [1], refers to the condition of bounded energy, the finiteness of the integral of the squared velocity of the fluid in the whole space
A way I see to prove the breakdown solutions of Navier-Stokes equations, following the described in [1], refers to the condition of bounded energy, the finiteness of the integral of the squared velocity of the fluid in the whole space.We can certainly construct solutions for ∂ui ∂t + Σ3j=1u j ∂ui ∂x j = v∇2ui − ∂p ∂ xi fi,1 ≤ i
Developed the foregoing, our example 3, which seeks a unique solution to the Navier-Stokes system with n=3, all terms of the equation, nonzero external force, and provides infinite total kinetic energy to the system (1) to (6) in t > 0will be based on the example 2, but again need to resort to the absence of non-linear term in the equation auxiliary with n=3
Summary
A way I see to prove the breakdown solutions of Navier-Stokes equations, following the described in [1], refers to the condition of bounded energy, the finiteness of the integral of the squared velocity of the fluid in the whole space
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
