Global Journal of Researches in Engineering, I: Numerical Methods, Volume 23 Issue 1

Equation (I) is confirmed to provide the left hand limit at = 0 . We have two problems here. One is the solution for the Euler equation when = 0. The solution is obtained by solving for one of the constants 6 . There are six unknown constants in the solution of the above PDE when = 0 . ( , = 1,2, …6) We use the fact that in the space ℑ( 3 , ) , the set {1, 1 , 1 2 } is linearly independent, implying that all the constants are zero in the solution except 3 and 4 associated with variables 3 , respectively. The solution is expressed as linear sums of the spatial and time variables. Now 3 is within an epsilon ball. The variable appears in the initial condition when solving for the unknown constant 6 , and the initial condition for 3 is given as the sum of arbitrarily large data and sums of reciprocal degenerate Weierstrass P functions in the three directions for small . We obtain the following solution, $ = ln −6 $ S : − 6 S S : − 6 :: − 2 $: − 2 $ S S − 2 $ S S − 2 $ : S − 2 S : − 2 S : S + e ¸ ] ¸ ¹ ¸ º : S = 12( + /2) : S + 12 $ /6 + S /6 : + 12 $ S + S S $ S + S S + : S e _¸ ] ¸ ¹ ¸ º C : : C m C ¼ − C : Global Journal of Researches in Engineering Volume XxXIII Issue I Version I 52 Year 2023 © 2023 Global Journals ( ) I Exploring Finite-Time Singularities and Onsager’s Conjecture with Endpoint Regularity in the Periodic Navier Stokes Equations Figure 1c: Linear functions in the form 3 = (− ( ) + ( ∗ − 600), > 0, , y-intercept. It is shown that the right side limit approaches infinity as → 1