Sentence examples for initial data in the from inspiring English sources

Initial data in the director has been added from outsourced writers in India.

Firstly, we establish that the solution is global in time under certain initial data in the stable set.

Let us state the existence result for the transport equation with initial data in the Besov space.

They prove the global existence of solutions with initial data in the potential well and show that every global solution is uniformly bounded in the natural phase space.

Moreover, they obtained that the solutions with positive initial energy blow up in a finite time for certain initial data in the unstable set.

Conversely, for certain initial data in the unstable set, there are solutions with positive initial energy that blow up in finite time.

Under suitable hypotheses on the continuous delay, distributed delay, and the initial data in this paper, the large-time behavior for the 2D Navier-Stokes-Voigt equations with continuous delay and distributed delay on the Lipschitz domain is studied.

The initial data in this case is given by textstylebegin{cases} (rho,v_{i},p)=(1,0,1) &text{if }rle0.4, (rho,v_{i},p)=(0.125,0,0.1) &text{otherwise}, end{cases} where r is the distance from the origin.

Herta Flor's group [ 99] provided the initial data in this area.

In this paper, we prove that for every nonnegative initial data in L1 R2), the Patlak Keller Segel equation is globally well-posed if and only if the total mass M≤8π.

Among other things, we provide a necessary and sufficient condition on the initial data in order that the solution exist for all time and remain non-negative.