Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating

Table 1

Various states of Landau equation.

Linearly stable (subcritical region) $d_i<0$	Subcritical instability $E_1<0$	$\epsilon a_0<{(d_i/E_1)}^{1/2}$	$a_0\to 0$	Conditional stability
		$\epsilon a_0>{(d_i/E_1)}^{1/2}$	$a_0\uparrow$	Subcritical explosive state
	Subcritical (absolute) stability $E_1>0$	$a_0\to 0$
Linearly unstable (supercritical region) $d_i>0$	Supercritical explosive state $E_1<0$	$a_0\uparrow$
	Supercritical stability $E_1>0$	$\epsilon a_0\to {(d_i/E_1)}^{1/2}$
		$N{c}_r\to d_r+d_i(F_1/E_1)$