Recently I saw How the Universe Works. In one of the episodes, concerning Jupiter, they told that the storms on Jupiter can survive many, many, times longer than those on Earth.
What is the reason behind it? They said that it is due to its big mass. But how can mass determine the survival of a storm?
I also want to know why Jupiter is so big and other planets are not.
In addition to answer of Autolatrty, you might want to take a look here at an experiment by Harry Swinney at U. Texas in Austin
This experiment simulated the atmosphere of Jupiter and found that there was always one 'stable' vortex like Jupiter's red spot. If ever two were formed then they would quickly combine together to form one.
This is a classic experiment in the area of 'Chaos and Non-Linear Dynanics' and provides an explanation as to why the red spot of Jupiter is always present.
“Lacking any… surface” (see Autolatry’s answer) in Jupiter is, first, dubious (a metallic hydrogen mantle is conjectured) and second, not very important per se. For example, Uranus and Neptune almost certainly have a relatively dense mantle with a sharp upper boundary, that doesn’t preclude these planets to have very long-living vortices in the atmosphere. How deep such a “surface” is situated may influence longevity of storms.
Important difference between Earth and giants planets is that Earth’s atmosphere is shallow and sparse, whereas giants’ atmospheres are thick and dense. Why does greater density prolong existence of vortices? Mainly because dense fluids tend to have lower kinematic viscosity (dynamic viscosity changes weakly on isothermal compression/decompression, whereas kinematic viscosity is dynamic viscosity divided by density). Dependence on depth is because a shallow fluid layer above a stationary solid exhibits greater shear rate (for similar motion speeds) and hence faster dissipation.
Circulation in the Jovian atmosphere is different from Earth because the interior of Jupiter is fluid and lacks any solid surface so convection may occur throughout the planet's outer "molecular envelope". The vortices on Jupiter are such that since they are so large they can last from 1-3 years.
On Jupiter anticyclones (in general) form through the merging of smaller structures including convective storms within "zones" toward the equator. The Great Red Spot is an example of this type of anticyclone,
