Hi there. I'll first start by saying that I have not studied the Mongol Empire in any professional setting (as of yet), but do considerable reading on them when I get the chance. That being said, I'll answer your question to the best of my abilities - However, it should also be noted that your question can be interpreted in a couple ways as in, 'Why didn't the Mongols mount an invasion of South East Asia?' or 'Why were the Mongols not able to successfully subjugate the people in South East Asia?". I'll try both.
For the first, asking why they did not attempt to conquer South East Asia, they did try to, and on three separate occasions. The first occurred not long after Genghis Khan's death, only 31 years after in fact. By 1258, the Mongols now under the leadership of Genghis's grandson Möngke were nearly finished with the conquering of China. However, due to the terrain in parts of Southern China, especially what is now Yunnan, being incredibly mountainous, it became difficult for the large, mobile armies of the Khan to travel. It was in this year that one of Möngke's generals sent an envoy to the Kingdom of Dai Viet - modern day northern Vietnam - requesting military access. Upon their arrival at the Emperor Trần Thái Tông , they were imprisoned; the next two successive envoys sent by the Mongols would also be detained. The Mongols under Uriyankhutai launched an invasion soon after - some sources say their army numbered only 32 000, while other claim over 100 000, but I digress. An ensuing battle between the Vietnamese and Mongols was a disaster for the defenders. The Vietnamese war elephants panicked in the heat and confusion of battle and wreaked havoc in their own lines. Trần Thái Tông who was present at the battle and reportedly led his own men atop one of these elephants was able to escape to a nearby island, safe from the Mongol horde who, without boats, could not reach him. Unfortunately, the destruction of the Vietnamese army left their capital undefended. One might be led to believe that this would indeed mean that the Mongols succeeded in conquering Vietnam with its Emperor fleeing and capital vulnerable, but for a still unknown reason, Uriyankhutai and his horsemen left Vietnam only days later, having been apparently ordered to return to China for another war against the remnants of the Song dynasty.
The second and third invasions were not carried out by the true Mongol Empire per se, but by the Yuan dynasty headed by Kublai Khan, which was one of the successor states that emerged after the rather violent division of the Mongol Empire (but that's a story for another time). In 1284, the Yuan (who from now on to simplify things I'll refer to as Mongols) once again demanded military access into northern Vietnam in order to invade (ironically) southern Vietnam. Although the Emperor of Vietnam agreed to this, one of his generals did not. General Hưng Đạo levied around 15 000 to assist the southerners in repelling the invasion. All the while, the Emperor instituted a scorched earth policy against the invaders, denying them food sources, lodgings, and most importantly for a mobile army, intact infrastructure. The Mongol campaign dragged on far into the sweltering heat of Summer and their troops grew exhausted, partly from the climate and partly from the efforts of the Vietnamese to make their lives awful. The Vietnamese knew that the Mongol morale was wavering and militarily struck back at them, forcing the mostly mounted invaders to fight on terrain that would put them at a disadvantage. One of the Mongol armies was nearly completely decimated, with one of their leading generals being slaughtered, but the other was able to escape with the help of the Yuan navy. The third fared no better. Despite trying a new strategy of setting up a main base of operations in Vietnam to launcher further invasions into the interior, the Mongols were faced with another war of attrition. The Vietnamese continued to pull back, leaving the invaders with just deserted, burnt farmland to conquer - no food, no pastures, no where to properly set up camp. Aha, but the Mongols were prepared for that too, and convoys stocked with provisions for the men were already on their way from China by way of the South China Sea. If only they were not ambushed by the Vietnamese fleet at Bạch Đằng and annihilated. The Mongol army, without supplies, was forced to retreat back to China.
So, to answer your question, they did try to conquer South East Asia, but the first step to do so, Vietnam, never submitted. To answer the second as to why it never came to fruition, one could argue it was cunning tactics, the geography, staunch resistance, or a combination of all three. However, the reason said each time was often linked to a lack of supplies, which either forced the Mongols into situations that they could not win, or led them to give up and just go home (as seen in the final invasion). I hope this answers your main question.
Bibliography
Chapuis, Oscar. A history of Vietnam: from Hong Bang to Tu Duc. Westport: Greenwood Press, 1995.
Karnow, Stanley. Vietnam: a history. New York: Penguin Books, 1984.
Alright, well, let’s get one thing straight right off the bat – the Mongols, or at least the shard of them under Khubilai Khan known as the Yuan Dynasty of China – absolutely did try to conquer Southeast Asia, including all of the territories you mentioned. And not only once, but several times. So, the real question is not “why didn’t they,” but rather “why didn’t it work there, then… when they had already managed to achieve much greater victories?”
So first, let’s deal with the rationales of why Khubilai of the Toluid House of Clan Borjigin, felt compelled to expand to the south. There are the nominal answers (which have validity, I’m not denying that) of the Great Mongol Khanate understanding that it had the express mandate to control the entire Earth, and seeing all foreign states as vassals whether they liked it or not. There is at least a ceremonial excuse in that. However, it was not the case, really, with Khubilai – or any of the Mongol khanates for that matter, that this point. Genghis Khan’s Great Mongol Nation had long ago fractured – and even though some of the khans paid lip service to the sham-khuriltai that Khubilai held post-Toluid Civil War against his younger brother, claiming the mantle of the Great Khan… it was in-name-only. Khubilai and all the rest had long ago had to come to terms with the simple fact that none of them were going to “rule the four corners of the World” or anything quite so grandiose.
Instead, Khubilai was from the outset beset with a kind of “imposter syndrome.” Though born of the steppe, he had lived most of his life, and even his childhood, in northern China, surrounding by a panoply of Chinese, Khitan, Jurchen, Uyghur, Tibetan, etc caretakers and advisers. In many ways, this made him a far better and more balanced ruler than his Central Asian kinsmen. Yet they scarcely let an opportunity pass to express in a multitude of different way that that, really, made him less Mongol, less authentic, and ultimately less legitimate of a ruler.
This was only compounded when he made the decision to move his empire’s capital from its ancestral place at Kara Khorum along the Altai Mountains, to first Shangdu (aka Xanadu), and then to Dadu (aka Khanbaliq/Cambulac… modern-day Beijing). By moving the capital into China proper, rather than the land of the Mongols, he had made a powerful statement to his Chinese subjects that he was prepared to truly become their Emperor, rather than remain an aloof, foreign Khan. This was much to his benefit in many respects – but that sword cut both ways, as it served as – Aha! – proof-positive that Khubilai was “going native” and losing touch with his roots (and therefore his right to rule). Shortly thereafter, a running civil war would break out between Khubilai and his cousin, the Khan of the Ogedeids, Khaidu, who charged that he was no true khan and could not hope to command real Mongols’ allegiance. The war between them – reformer versus traditionalist – would rage on and off for the remainder of both of their lives.
So, suffice it to say that Khubilai was a little sensitive about proving his bona-fides as a “real true Mongol.” And the surest way to show one’s merit as a Mongol commander was in doing like Grandfather Genghis had done, and crushing your enemies, seeing them driven before you, and hearing the lamentations of their women.
Yet, for all that, Khubilai by the mid-1280s was – both personally and in terms of his empire’s mojo – simply running out of steam. It all began with Japan – that string of islands so close to long-conquered Korea that it seemed you might be able to hit it with a thrown stone. Yet try as he may – first in 1274 and again in 1281 – Great Yuan, for all is terrifying might, simply could not sink the putt. Quite infamously, both times the Japanese defenders were greatly aided by unseasonable storms and typhoons hitting almost exactly as the Sino-Mongol forces made landfall, smashing the Korean-captained ships against the coastal rocks, and stranding the armies to be mopped up to a man by the Shogunate’s samurai legions. This is the origin of the Japan legend of the “divine winds” – the kamikaze – that would rise up to defend Japan against any foreign invasion. A third invasion was planned for 1286, but due to financial constraints (and further humiliating defeats to the south that we’ll get to in a moment) he was forced to call it off.
This was more than mere setback, this was an abject humiliation. This called into question not only his competence as the ruler of Great Yuan, but shattered the near-mythical perception of Mongol invincibility across the region. Prior to this, Khubilai had been able to quote Thanos and say, “I Am Inevitable.” Yet now, not just once, but twice, the Japanese had thrown his best efforts back – and at the cost of tens- to hundreds-of-thousands of lives. He was, in fact, Evitable.
At least as damaging as the loss of the psychological force-field, though was the tremendous expense of this now-failed undertaking. The Yuan had, effectively, run out of juice. Khubilai had become so focused on the military conquest of Japan, no matter the cost, that the costs finally overran his ability to ignore them. His prestige and his finances were both “squandered in these campaigns. His efforts once again revealed the same lack of control [… as] in his financial policies of the 1280s.”
In his personal life, as well, Khubilai was dealt a 1-2 combo of heartbreak. The death of his empress, confidant, truly better-half, and love of his life, Chabi in 1281 had left him “wretched and alone.” But the unexpected death of his son and chosen heir, Crown Prince Zhenjin in 1285 at only 43-years-old was an unmitigated disaster for Khubilai personally, and like as not also an unrecoverable loss for the realm at large. Suddenly without his heir at near 70, the loss truly seems to have utterly broken what was left of Khubilai’s soul after Chabi’s death. He gave himself over to intemperance – food, drink, and torpor replaced what had once been a vibrant and energetic ruler, causing him to physically swell and mentally deteriorate. In effect, for the final decade-and-a-half of his reign, Khubilai was "Governing Under the Influence" of possibly the most toxic combination of chemicals: grief and booze. Yet for all that, he nevertheless was compelled to continue on his life’s work of continual conquest and additional legitimacy for he and his successors.
Hey there,
Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.
If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!
The Mongolian actually almost took Vietnam successfully in their first time. But, somehow our ancestors learnt that all they need to do is leaving Thang Long, which is vietnamese capital at the moment. When they left, they burnt down all the food, took the animals with them, and some source said that they even put the poison into the water, i don't remember the poison is true or not. But anyways, the invaders got no food, they also had to fight against the disease in a tropical country. When they were weakend enough, Vietnamese fought them in a big battle and won against the Mongolian. Their second invade was not different from the first one, they did it with a bigger army. Their third time was way more dangerous than the other two, because they learnt that they should have food with them to prevent the Vietnamese to do the same trick again. So they sent their food with the marine escort it. Vietnamese did the same trick again, as what the Mongolian has predicted. Also, we still had some tactic to deal with them on Bach Dang river. We put some pales inside the river and lured them into the pales during the time that the water in the river is lowest. That is the tactic that Ngo Quyen king used to deal with Chinese in 981 on the same river. When they had lost their rations, everything turned out to be the same as the first two times. About the Mongolian invades, their army moved so fast because they don't bring a lot of rations with them, they would take it from the country that they invaded. We was both lucky and smart enough to find their weakness is the rations. So we had stopped them and protected our land and people.