The present paper aims at studying the contribution of the second-ordered spatial derivative term to the well-posedness of the two fluid model with single pressure. A numerical experiment based on Hadamard's condition demonstrates that the second-ordered spatial derivative in the momentum equation can make the system well-posed for an initial value problem without regard to the magnitude of the term. Consideration on the eigenvalues has an advantage of knowing the movement of the system from being ill-posed to well-posed.It is derived analytically that the maximum of the real part of eigenvalues is intensively dependent on the wave number and is inversely proportional to the coefficient of the second-ordered derivative.

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