what is the condition to use the wave equation?
I am searchig for this question: what is the condition to use the wave equation? or what is the difference between the wave equation and navier- stockes equation? I could derive the wave equation from the navier-stockes equations with this hypothesis that the effect of viscosity is zero, but i want to know that for example can we use the wave equation for all mach numbers? I explain more: for example in blast or explosion that we have shock wave that the mach number is grater than 1 and the pressure gradient is very high can we use wave equation or we mast use navier stockes equations only to capture this phenomena? I need to have more mathematic informations,for examle this answer that up to 0.99 mach number we can use wave equatin and for upper this value we cannot use wav equation and also information about pressure gradient condition and ets ....
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