The Burgers’ equation with stochastic transport: shock formation, local and global existence of smooth solutions
2019 ◽
Vol 26
(6)
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Keyword(s):
Blow Up
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Abstract In this work, we examine the solution properties of the Burgers’ equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine–Hugoniot condition that the shocks satisfy. Next, we establish the local existence and uniqueness of smooth solutions in the inviscid case and construct a blow-up criterion. Finally, in the viscous case, we prove global existence and uniqueness of smooth solutions.
1997 ◽
Vol 127
(5)
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pp. 935-946
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1999 ◽
Vol 155
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pp. 55-80
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2020 ◽
Vol 28
(1)
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2010 ◽
Vol 20
(supp01)
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pp. 1425-1457
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2017 ◽
Vol 47
(7)
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pp. 2365-2394
2011 ◽
Vol 377
(2)
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pp. 534-539
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Keyword(s):
2010 ◽
Vol 11
(5)
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pp. 3555-3566
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