Abstract
In this work, we investigate the Cauchy problem for a generalized Riemann-type hydrodynamical equation. The local well-posedness of the equation in Besov spaces is derived by using Littlewood–Paley decomposition and transport equation theory. Then, we show that a finite maximal life span for a solution necessarily implies wave breaking for this solution and give a condition on the initial data to ensure wave breaking for this equation by making use of the method of characteristics; otherwise, the equation has a global smooth solution. In addition, we establish persistence results for solutions of the equation in weighted Lp spaces for a large class of moderate weights.
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