Water Wave Equation Arising On Logarithmic Quantum Mechanics

We introduce the model of equation that is closely related to the following equation (1.1). We study the global existence of week solution for this class of equation. Using the Gross logarithmic Sobolev inequality we establish the main theorem of existence of week solution for this class of equation arising from Logarithmic Quantum Mechanics. We can extend the results of [1, 2].