The fate of the dwarves in LOTR is not explicitly stated in the books or movies, but there are some indications in the appendices and other sources. Here are some key points from the search results:

• After the defeat of Sauron, the dwarves helped to restore Middle-earth and forged a new kingdom under Gimlis leadership.
• The dwarves fought against Saurons army in various places, including the Battle of Dale.
• The dwarves of Erebor helped to rebuild many of the flattened cities of Gondor.
• The dwarves slowly began to fade away like the elves before them, and none sailed into the West except for Gimli, who was given passage by the elves.
• There is a suggestion in one text that the line of the dwarves eventually came to an end, although this was not until the world had grown old.
• The dwarves were largely absent from the main conflict in LOTR, but they were busy fighting their own battles for the War of the Ring.

In summary, the dwarves played a significant role in the events leading up to and during LOTR, but their fate after the defeat of Sauron is not fully known. They helped to rebuild Middle-earth and fought against Saurons forces, but they slowly faded away over time.