Question: What son of Grand Duke Lithuania Kęstutis went on to defeat Švitrigaila and his Livonian allies?

Context paragraphs:
Lithuanian Civil War (1432–38): The Lithuanian Civil War of 1432–1438 was a conflict over the succession to the throne of the Grand Duchy of Lithuania, after Vytautas the Great died in 1430 without leaving an heir.  The war was fought on the one side by Švitrigaila, allied with the Teutonic Knights, and on the other by Sigismund Kęstutaitis, backed by the Kingdom of Poland.  The war threatened to sever the Union of Krewo, the personal union between Poland and Lithuania.  Švitrigaila's alliance with the Grand Master of the Teutonic Order, Paul von Rusdorf, launched the Polish–Teutonic War (1431–1435) but failed to secure victory for Švitrigaila.

Lithuanian Crusade: The Lithuanian Crusade was a series of campaigns by the Teutonic Order and the Livonian Order, two crusading military orders, to convert the pagan Grand Duchy of Lithuania into Roman Catholicism.  The Livonian Order settled in Riga in 1202 and the Teutonic Order arrived to Culmerland in 1230s.  They first conquered other neighboring Baltic tribes – Curonians, Semigallians, Latgalians, Selonians, Old Prussians (see Livonian Crusade and Prussian Crusade).  The first raid against the Lithuanians and Samogitians was in 1208 and the Orders played a key role in Lithuanian politics, but they were not a direct and immediate threat until 1280s.  By that time the Grand Duchy of Lithuania was already an established state and could offer organized defense.  Thus for the next hundred years the Knights organized annual destructive "reise" (raids) into the Samogitian and Lithuanian lands but without great success: border regions in Samogitia and Suvalkija became sparsely inhabited wilderness, but the Order gained very little territory.  The Grand Duchy finally converted to Christianity in 1386, when Grand Duke Jogaila accepted baptism from Poland before his wedding to reigning Queen Jadwiga and coronation as King of Poland.  However, the baptism did not stop the crusade as the Order publicly challenged sincerity of the conversion at the Papal court.  Lithuania, together with its new powerful ally Poland, defeated the Order in the decisive Battle of Grunwald in 1410, which is often cited as the end of the Lithuanian Crusade.  The final peace was reached by the Treaty of Melno (1422).

Lithuanian Civil War (1389–92): The Lithuanian Civil War of 1389–92 was the second civil conflict between Jogaila, King of Poland and Grand Duke of Lithuania, and his cousin Vytautas.  At issue was control of the Grand Duchy of Lithuania, then the largest state in Europe.  Jogaila had been crowned King of Poland in 1386; he installed his brother Skirgaila as ruler of Lithuania.  Skirgaila proved unpopular and Vytautas attempted to depose him.  When his first attempt to take the capital city of Vilnius failed, Vytautas forged an alliance with the Teutonic Knights, their common enemy – just as both cousins had done during the Lithuanian Civil War between 1381 and 1384.  Vytautas and the Knights unsuccessfully besieged Vilnius in 1390.  Over the next two years it became clear that neither side could achieve a quick victory, and Jogaila proposed a compromise: Vytautas would become Grand Duke and Jogaila would remain Superior Duke.  This proposal was formalized in the Ostrów Agreement of 1392, and Vytautas turned against the Knights.  He went on to reign as Grand Duke of Lithuania for 38 years, and the cousins remained at peace.

Michael Žygimantaitis: Michael Žygimantaitis (Lithuanian: "Mykolas Žygimantaitis" , Polish: "Michał Bolesław Zygmuntowicz" ; before 1406 – shortly before February 10, 1452 in Moscow) was the last male descendant of Kęstutis, Grand Duke of Lithuania.  He supported his father Sigismund Kęstutaitis in power struggles with Švitrigaila.  In 1435 he led his father's army to victory in the Battle of Pabaiskas.  After his father's assassination in 1440, Michael unsuccessfully fought against Casimir IV Jagiellon for the title of the Grand Duke of Lithuania.  At first Michael was supported by Samogitia, but in 1441 Casimir issued a privilege confirming Samogitia's semi-autonomous status and thus avoiding a civil war.  Until 1447 he was supported by Dukes of Masovia.  In 1448 Michael asked help from the Crimean Khanate.  With their help he attacked and shortly took control of Kiev, Starodub, Novhorod-Siversky.  Soon he was captured and transported to the Grand Duchy of Moscow where he died under unclear circumstances (possibly poisoned).  He was buried in Vilnius Cathedral.

Treaty of Christmemel: The Treaty of Christmemel (Lithuanian: "Skirsnemunės sutartis" ) was a treaty signed on 19 June 1431 between Paul von Rusdorf, Grand Master the Teutonic Knights, and Švitrigaila, Grand Duke of Lithuania.  Švitrigaila was preparing for a war with Poland to defend his claim to the Lithuanian throne and sought allies.  The treaty established an anti-Polish alliance and prompted the Knights to invade the Kingdom of Poland, starting the Polish–Teutonic War (1431–35).  Lithuania also surrendered Palanga and three miles of the coastline on the Baltic Sea, thus modifying the Treaty of Melno of 1422.

Vaišvilas: Vaišvilas (Polish: "Wojszwił") (14th century) was a Lithuanian noble and sometimes is considered as one of the sons of Kęstutis, Grand Duke of Lithuania.  In 1358 Kęstutis and Masovian princes formed a commission to settle border disputes.  The Lithuanian side was represented by Vaišvilas (Woyszwylt), Patirgas, possibly another son of Kęstutis, and Eikšis, son of Karijotas.  This leads historians to believe that Vaišvilas ruled some area bordering Masovia.  In 1367 a treaty with Livonia mention Vaišvilas as "Waysewist".  Later he is found in Lahojsk, now Belarus.  There are theories that an unnamed "nobilis satrapa" who died at the Battle of Rūdava in 1370 was Vaišvilas.  He probably died before 1385 or 1387 because he is not mentioned during turbulent civil wars between Vytautas the Great and Jogaila.

Lithuanian Civil War (1381–84): The Lithuanian Civil War of 1381–1384 was the first struggle for power between the cousins Jogaila, Grand Duke of Lithuania and later King of Poland, and Vytautas the Great.  It began after Jogaila signed the Treaty of Dovydiškės with the Teutonic Knights which was aimed against his uncle Kęstutis, father of Vytautas.  Kęstutis briefly seized power in the Grand Duchy, but was betrayed by adherents of Jogaila primarily from Vilnius.  During negotiations for a truce Kęstutis and Vytautas were arrested and transported to the Kreva Castle.  Kęstutis died there a week later but Vytautas managed to escape and then sought an alliance with the Teutonic Knights.  Subsequently their joint forces raided Lithuanian lands.  Eventually the cousins were reconciled as Jogaila needed internal stability in anticipation of negotiations with the Grand Duchy of Moscow and the Kingdom of Poland regarding the possible Christianization of Lithuania.  The war did not settle the power struggle; it continued during the next Lithuanian Civil War (1389–1392) which was resolved by the signing of the Ostrów Agreement.  After more than ten years of struggle, Vytautas finally became the Grand Duke of Lithuania and ruled the country for thirty-eight years.

Peace of Brześć Kujawski: Peace of Brześć Kujawski was a peace treaty signed on December 31, 1435 in Brześć Kujawski that ended the Polish–Teutonic War (1431–1435).  The treaty was signed in the aftermath of the Livonian Order's defeat at the hands of the allied Polish-Lithuanian force in the Battle of Pabaiskas (Wiłkomierz).  The Teutonic Knights agreed to cease their support to Švitrigaila (who tried to break the Polish-Lithuanian union) and in the future to support only Grand Dukes properly elected jointly by Poland and Lithuania.  The treaty did not change borders determined by the Treaty of Melno in 1422.  The Peace of Brześć Kujawski showed that Teutonic Knights lost their universal missionary status.  Teutonic and Livonian Order no longer interfered with Polish–Lithuanian affairs; instead Poland and Lithuania involved themselves in the Thirteen Years' War, the civil war in Prussia that tore it in half.

Sigismund Kęstutaitis: Sigismund Kęstutaitis (Lithuanian: "Žygimantas I Kęstutaitis" ; Polish: "Zygmunt Kiejstutowicz" ; c. 1365 – 20 March 1440) was the Grand Duke of Lithuania from 1432 to 1440.  Sigismund was his baptismal name; Sigismund's pagan Lithuanian birth name is unknown.  He was the son of the Grand Duke of Lithuania Kęstutis and his wife Birutė.

Battle of Wilkomierz: The Battle of Wilkomierz (see other names) took place on September 1, 1435 near Ukmergė in the Grand Duchy of Lithuania.  With the help of military units from the Kingdom of Poland, the forces of Grand Duke Sigismund Kęstutaitis soundly defeated Švitrigaila and his Livonian allies.  The battle was a decisive engagement of the Lithuanian Civil War (1432–38).  Švitrigaila lost most of his supporters and withdrew to southern Grand Duchy; he was slowly pushed out and eventually made peace.  The damage inflicted upon the Livonian Order has been compared to the damage of Battle of Grunwald upon the Teutonic Order.  It was fundamentally weakened and ceased to play a major role in Lithuanian affairs.  The battle can be seen as the final engagement of the Lithuanian Crusade.

Supporting paragraphs: Battle of Wilkomierz Sigismund Kęstutaitis
Answer: Sigismund Kęstutaitis