Explain the eulers equation

Question

Solve the following equation:

Start from Euler's equation
∂v/∂t + (v · ∇)v + ∇p = 0 with divv = 0

Take the divergence to obtain ?p as a quadratic expression in ∂v
∂x = ( ∂v_i ∂xj).

Use divv = 0 to make this as simple as you can. Assuming v and p vanish sufficiently rapidly at ∞, express p itself in terms of v alone. In this case ?p = whatever determines p only up to an additive harmonic function, then use the fact that p(0) = 0 to get rid of it.