Jennifer Lind is associate professor of government at Dartmouth College. The opinions expressed in this commentary are hers.

(CNN) As North Korea develops an intercontinental nuclear capability, President Donald Trump has veered from forbearance to frustration regarding China's role. Earlier this summer Trump told Chinese President Xi Jinping, "I appreciate the things that you have done" on North Korea; more recently, however, his tweets have been laced with irritation. "They do NOTHING for us with North Korea, just talk," Trump declared . "We will no longer allow this to continue. China could easily solve this problem!"

Beijing may have temporarily mollified the Trump administration, which was pleased by Chinese support for tighter UN sanctions against North Korea. But despite Washington's hopes, China won't solve the North Korea problem, regardless of how often the Trump administration insists that it can or must.

To be sure, Beijing has leverage over Pyongyang; trade with China comprises 90% of North Korea's trade, including vital imports such as food and oil. Furthermore, North Korean businesses have set up joint ventures with Chinese firms, which allow Pyongyang access to the global economy. Beijing could crack down on these relationships.

While China has leverage, it won't use it to pressure North Korea. As I found in recent conversations with scholars and government officials in Beijing, the Chinese diagnose the problem and its solution very differently, and have very different interests at stake.

The Americans see North Korea as a dangerous rogue state that broke international law to acquire nuclear weapons. But China sees North Korea as motivated by insecurity. The Chinese say that because the United States and South Korea are so much more powerful, and because the United States goes around the world toppling governments, it's no wonder that Pyongyang wants nuclear weapons. In their view, North Korea is not the menacing rogue state; America is. "You need to understand," several people in Beijing told me, "the Americans are the source of their fear."

How to solve the problem? The Chinese feel "unfairly burdened" (as a recent China Daily op-ed said) at being seen as the key to a solution. In their view, Washington, not Beijing, is the key; only the Americans (by reducing North Korea's fear) can influence Pyongyang.

The Chinese urge the United States to stop the military exercises with South Korea that frighten the North, give security assurances to Pyongyang, and withdraw military forces from South Korea. (Washington does not see these as bargaining chips but as essential for maintaining readiness and deterrence on the peninsula.)

China also has very different interests at stake. While North Korea's intercontinental nuclear capability is a game-changer for the Americans, it isn't for the Chinese, who have already been living with North Korean nuclear weapons.

China worries most about political stability on the Korean peninsula. The Chinese fear that serious economic pressure would risk causing Kim Jong Un's regime to collapse, which could unleash chaos on the peninsula, and usher in a variety of long-term problems.

The Chinese worry that North Korean regime collapse would send refugees flooding across their border, and are alarmed by the prospect of military intervention by South Korea and the United States. Bruce W. Bennett of RAND and I modeled the requirements for military missions in a post-collapse North Korea: for example, humanitarian relief, border control operations, and missions to find "loose nukes." Performing these missions would require hundreds of thousands of troops.

Imagine this scenario from China's perspective: the prospect of serious instability, and massive military intervention by two powerful armies, right on its border. Because China intends to intervene as well, this scenario has the potential for dangerous escalation. This -- not a North Korean intercontinental strike capability -- is Beijing's nightmare.

Then there are the longer-term concerns. The Chinese face a potential demographic problem in Jilin province, in Yanbian autonomous prefecture, where a substantial amount of the population is ethnically Korean. (Many North Koreans fled there during the years of famine.) Beijing worries that the area's demographics will become too Korean, encouraging secessionist feeling. The Chinese Communist Party already has enough of this on its hands in Tibet, Xinjiang, and Taiwan.

North Korean collapse, and Korean unification, also have implications for the broader military competition between China and the United States. North Korea currently provides a buffer between China and American troops in South Korea.

The Chinese fear that if Korea unifies, American troops would remain, and China would lose this buffer. The Chinese also say that they like that North Korea preoccupies US diplomacy, military planning, and force structure: that without the North Korean thorn in the American side, Washington might turn its gaze toward Taiwan and the South China Sea.

Thus while the Chinese certainly would prefer that North Korea not have nuclear weapons, their greatest fear is regime collapse. "At times China will probably put more pressure on North Korea," one Chinese scholar told me, "but we will not fundamentally change our position."

Getting Beijing to act against its own interests will be hard, if not impossible, and will require more than frustrated tweets ( dismissed by China's state media as "emotional venting"). To get China to act against its own interests, the Trump administration would have to make a deal. What does China want that Washington could give it?

But a deal acceptable to both sides probably doesn't exist. The sorts of carrots, capitulations, or concessions that Washington would have to dangle at Beijing would have to be big -- really big (perhaps related to the US-Japan alliance, South China Sea, or Taiwan). But, with its many treaty allies and interests in East Asia, Washington would be unwilling to offer that kind of carrot.

Which brings us to sticks. The Trump administration could try to convince Beijing that Washington simply will not live in a world with a North Korean intercontinental strike capability: that if Beijing won't help try economic coercion, the administration will use force against North Korea.

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