Global Well-posedness For The Korteweg-de Vries-Burgers Equation

In natural science and social science, the nonlinear science is playing an increasingly important role. Therefore, there is an increasing focus on such issues. Many people find that a large number of nonlinear problems of research need to be converted to nonlinear evolution equations to express and elaborate. This harmonic analysis method for the generation and development has laid a theoretical and practical basis, so as to promote the application of this approach harmonic analysis and development of nonlinear evolution equations. Many new operator class and new function space framework are discovered and applied by people in the study of nonlinear evolution equations.Condering the cauchy problem for the fifth-order Korteweg-de Vries-Buegers equation(the fifth-order KdV-B equation): is a very important physical and mathematical models. It has been derived as a model for the propagation of weakly nonlinear dispersive long waves in some physical contexts when dissipative effects occur. In this paper, we mainly through the construction of new function space, and show that it is locally well-posed in Hs(s>sα) by Bourgain space theory and [k;Z]-multiplier, sα=-7/4, when 0<α≤3/2; sα=-1-α/2, when 3/2<α≤2. Then, again in accordance with infinitely smooth and conservation of structure of fifth-order KdV-B equation, we can use the standard method, and extend the existence interval of solutions to [0,+∞], resulting in its global well-posedness.