As i know, After few years there is no Block Reward for miners, therefore the amount of all bitcoins in world does not increase anymore.
At that time, why should somebody do mining? and nobody do mining how we can trust Blockchain without proof of work?
Really an interesting question.
It may seem that the group of individuals most directly effected by the limit of the Bitcoin supply will be the Bitcoin miners themselves. On one hand, there are detractors of the Bitcoin limitation who that say that miners will be forced away from the block rewards they receive for their work once the Bitcoin supply has reached 21 million in circulation. In this case, these miners may need to rely on transaction fees in order to maintain operations. Bitcoin.com points to an argument that miners will then find the process unaffordable, leading to a reduction in the number of miners, a centralisation process of the Bitcoin network, and numerous negative effects on the Bitcoin system.
This argument assumes that transaction fees alone will be insufficient to keep Bitcoin miners financially solvent once the mining process has been completed. On the other hand, there are reasons to believe that transaction fees and mining costs will even out in the future. Looking ahead by several decades, it is not difficult to imagine that mining chips will become small and highly efficient. This would reduce the burden placed on miners and would allow mining to become an activity with a lower threshold of initial cost. Further, transaction fees may increase, and this could help to keep miners afloat as well.
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