The U.S. is faced with a troublesome question: Is it willing to challenge Chinese ambitions in the South China Sea to maintain a posture of exceptional military dominance there?

The reality is that China, as it grows in economic importance, including the holding of more than $1 trillion in U.S. debt, will seek to expand its influence in its region of the world. In particular, especially given the importance to it of both exports and imports, it will be interested in expanding its sea presence.

For all of its ambition, though, China spends only about 10 percent of what the United States does on its military.

Against that backdrop, the Chinese are seeking to reinforce their claims to the Spratly Islands, rocky outcrops in the South China Sea, by dredging and building installations there. Chinese neighbors Brunei, Malaysia, the Philippines and Vietnam also claim parts of the Spratlys and are looking to the United States to defend their interests.

The U.S. military is carrying out air missions over the Spratlys to defend their neighbors’ and American interests there, although the latter are difficult to define.

There is always the risk of an accident or a military confrontation occasioned by U.S. flights over the Chinese sites. But are the gains worth, first, the financial cost of carrying them out and, second, the risk of conflict with the Chinese in their own region?

It’s becoming harder for the Pentagon to make that case.