Global existence and Lp estimates for solutions of damped wave equation with nonlinear convection in multi-dimensional space

In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the Lp (2 ≤ p ≤ ∞) decay estimates of the solution.