FROM inside his headquarters in the southern Saudi city of Najran, Major-General Saad Olyan, the area commander, looks up at the craggy mountains looming over the city and wonders what Yemen’s rebels on the plateau above will do next. They have pushed Saudi forces out of some border posts, and forced the evacuation of more than 7,000 civilians from Saudi villages near the ill-marked frontier.

Saudi artillery rhythmically thumps suspected rebel positions. But it has not prevented them from regularly rocketing Najran and other border towns, killing 80 people, 25 of them in Najran. One Katyusha rocket fell a few yards away from General Olyan’s office; the windows were blown out, pitting his walls with shrapnel. Another blew out the glass front of a nearby hotel shortly before it was due to open. A banner with a picture of King Salman and his designated heirs declares forlornly: “We are all soldiers of the homeland.”

Residents of the area have fled to safer parts of the city. Kindergartens and homes near the military base lie in ruins. Bar the Pakistani workers obliviously playing cricket, the streets feel like a ghost town.

Saudi Arabia’s young defence minister, deputy crown prince and de facto ruler, Mohammed bin Salman, insists he is winning the war. His coalition has retaken Aden, Yemen’s southern port, and 80% of the country, he claims. But many of Yemen’s largest cities—Sana’a, Taiz and Ibb—remain in rebel hands. And with negotiations stalling (the resumption of talks set for January 14th has been indefinitely postponed), officials talk less of an early victory than a protracted war. “We’re looking at conflict management, not resolution,” says a confidant of the prince. “This problem can go on for years.”

For all the bluster of Saudi generals who vow to lead their troops into Sana’a if necessary, the campaign now has more limited goals, says the confidant. Saudi Arabia wants to send Iran and its regional clients a message that it will resist their regional push. With Iran holding sway through its proxies in Baghdad, Damascus and Beirut, Saudi Arabia is loth to let a fourth capital, particularly one in its back yard, go Iran’s way. But the campaign is now mostly about blunting the capabilities of the Houthis (a militia of Zaydis, a splinter Shiite sect concentrated in Yemen’s north) and their ally, Ali Abdullah Saleh, who until Saudi Arabia engineered his removal in 2012 was the Arab world’s longest-reigning ruler.

Together the Houthis and Mr Saleh make a formidable force. Whereas the former are guerrillas who model themselves on Lebanon’s Hizbullah, the latter commands Yemen’s Republican army, which has been fighting wars (including against the Houthis) for 25 years. Together they wield an arsenal of tanks, ballistic missiles and, at one point, even the odd fighter-jet. Houthi fighters head to battle carrying charms, such as keys and visas to paradise. Their preachers on satellite television call for re-establishing Zaydi rule across the border, not just over the three border provinces the Al Sauds seized in 1934 but even over Mecca farther north.

That is implausible given Saudi Arabia’s air power and network of allies. But some Saudis ask how their overfed armed forces would fare should battle-hardened Houthi fighters make even a limited push across the border. It says much about Saudi trepidation that General Olyan limits himself to defending Saudi territory; he says his troops make no attempt to attack the Houthi heartland of Saada governorate, just across the frontier.

Allies have offered help. Last month Kuwait sent a battalion to the Saudi side of the border. Pakistan has vouchsafed to come to the kingdom’s rescue, should it come under attack. And at the back of Najran’s airport, the Americans have provided a battery of Patriot air-defence missiles to knock out the score of incoming SCUDs that Mr Saleh has fired at the kingdom’s southern cities.

But the costs for Saudi Arabia are mounting. Eroding his plans for cutting the budget deficit, Muhammad bin Salman is reinforcing his forces inside Yemen. Yemeni refugees, too, have been spilling into the kingdom, to the tune of over half a million. Cross-border smuggling and infiltration, perhaps of Houthi fighters, says a Saudi officer, is higher than ever. Yemenis do not constitute a fifth column, but they complain that Saudi Arabia is refusing them health care. Some mutter about turning the kingdom into a republic.

The air campaign in Yemen is denting Saudi Arabia’s reputation. The death-toll of Yemenis is nearly 6,000, a “modest” number says a Gulf official, especially when judged against the carnage elsewhere in the region. Some recall that Yemen, like Afghanistan, has been a graveyard for many an invader. But prominent preachers from Saudi Arabia’s religious establishment egg the Al Sauds to confront, not compromise with, the region’s Shias. Salman al-Ouda, a critical cleric with a strong Wahhabi following, wonders what the point was of spending billions and taking thousands of dead “if it just left us where we started?”