Isolated Singularities of the 1D Complex Viscous Burgers Equation |
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Authors: | Lu Li |
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Institution: | (1) Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, UK |
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Abstract: | The Cauchy problem for the 1D real-valued viscous Burgers equation u
t
+uu
x
= u
xx
is globally well posed (Hopf in Commun Pure Appl Math 3:201–230, 1950). For complex-valued solutions finite time blow-up
is possible from smooth compactly supported initial data, see Poláčik and Šverák (J Reine Angew Math 616:205–217, 2008). It
is also proved in Poláčik and Šverák (J Reine Angew Math 616:205–217, 2008) that the singularities for the complex-valued
solutions are isolated if they are not present in the initial data. In this paper we study the singularities in more detail.
In particular, we classify the possible blow-up rates and blow-up profiles. It turns out that all singularities are of type
II and that the blow-up profiles are regular steady state solutions of the equation. |
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Keywords: | |
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