Abstract
We are concerned with the global existence of classical solutions for a general model of viscosity long-short wave equations. Under suitable initial conditions, the existence of the global classical solutions for the viscosity long-short wave equations is proved. If it does not exist globally, the life span which is the largest time where the solutions exist is also obtained.
Highlights
In this paper, we studied the global well-posedness of the solutions for the long-short wave systems with viscosity which describes the coupling between nonlinear Schrodinger systems and the parabolical systems
In 1977, Benney [2] presented a general theory for deriving nonlinear partial differential equations in which both long and short wave solutions coexist and interact with each other nonlinearly
In [20], Tsutsumi and Hatano studied the well-posedness of the Cauchy problems for one type of Benney equations
Summary
We studied the global well-posedness of the solutions for the long-short wave systems with viscosity which describes the coupling between nonlinear Schrodinger systems and the parabolical systems. We extended the results to the viscosity long-short wave equations of the general form,. Us, we can get the existence of the global classical solutions for the viscosity long-short wave equations. If it does not exist globally, we can get the life span (the largest time in which the solutions exist) with a more general f(v) in Rn. e studies about the life span are bound in literatures [3, 7, 9, 10, 12, 13, 18, 19].
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