We study oscillation properties and determining nodes of solutions of the Ginzburg-Landau equation (GLE), the Kuramoto-Sivashinsky equation (KSE), and the Navier-Stokes equations (NSE).; In the case of the GLE, we establish an upper bound for the winding number of any function on the global attractor around any point outside its range. In a related result, we prove that the asymptotic behavior of solutions is determined by their values at two sufficiently close points (determining nodes).; Using a similar method, we prove that the number of zeros of functions belonging to the global attractor of the KSE is uniformly bounded. The same is also true for their space derivatives of any order. The other results on the KSE concern determining nodes, oscillations of stationary solutions, and the backward blowup of solutions.; With a method, which can be applied also to other dissipative equations, we show that there exists {dollar}epsilon >{dollar} 0 such that every time periodic solution of the NSE with a period less than {dollar}epsilon{dollar} is necessarily stationary. We conclude the thesis by studying continuity properties of the time analyticity radius for solutions in a vicinity of a stationary solution.
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