Let [[PSI].sup.[lambda]] = [lambda][PHI] and rewrite the NSPK system (1.1)-(1.3) into the following form
Before stating our main result, we first recall the local existence of strong solution to the incompressible Euler equations (1.4) and the global existence of weak solution to the NSPK system (1.5)-(1.7).
Then for any 0 < T < [T.sub.*], the global weak solution (([n.sup.[lambda]], [u.sup.[lambda]], [[PSI].sup.[lambda]])) of the NSPK system (1.5)-(1.7) satisfies the following estimates
Theorem 1 describes the combined quasi-neutral and vanishing viscosity limit of the NSPK system (1.5)-(1.7) with well-prepared initial data.
, where the convergence of (local) smooth solution of the NSPK system with viscosity term [mu] [DELTA] [u.sup.[lambda]] + v[nabla] [divu.sup.[lambda]] to the smooth solution of the incompressible Navier-Stokes equations is obtained by using the convergence-stability principle.
Figure 1 presents the receiver of NSPK protocol described by SE-LTS.
The networked model of NSPK protocol can be presented as in Figure 2.
An example of testable intruder model of NSPK protocol is presented in Figure 3.
For the example of NSPK protocol, the finial result of reachable graph is presented in Figure 4.
For example, by using our algorithm, 304 test cases are generated to verify the security of NSPK protocol implementations.
Some test cases of the NSPK protocol are presented also and the MITM attack of NSPK is verified to be concluded in our test cases.