scholarly journals Existence and blow up of solutions to the $ 2D $ Burgers equation with supercritical dissipation

2020 ◽  
Vol 25 (3) ◽  
pp. 1169-1192
Author(s):  
Binbin Shi ◽  
◽  
Weike Wang ◽  
Keyword(s):  
Burgers Equation ◽  
Blow Up ◽  
Supercritical Dissipation

scholarly journals Blow up and regularity for fractal Burgers equation

2008 ◽  
Vol 5 (3) ◽  
pp. 211-240 ◽  
Author(s):  
Alexander Kiselev ◽  
Fedor Nazarov ◽  
Roman Shterenberg
Keyword(s):  
Burgers Equation ◽  
Blow Up

scholarly journals Blow-Up of the Hyperbolic Burgers Equation

2007 ◽  
Vol 127 (2) ◽  
pp. 327-338 ◽  
Author(s):  
Carlos Escudero
Keyword(s):  
Burgers Equation ◽  
Blow Up

scholarly journals Complex blow-up in Burgers' equation: an iterative approach

1996 ◽  
Vol 54 (3) ◽  
pp. 353-362 ◽  
Author(s):  
Nalini Joshi ◽  
Johannes A. Petersen
Keyword(s):  
Holomorphic Function ◽  
Series Expansion ◽  
Laurent Series ◽  
Burgers Equation ◽  
Blow Up ◽  
Meromorphic Solution ◽  
Iterative Approach ◽  
Painlevé Test ◽  
Formal Laurent Series

We show that for a given holomorphic noncharacteristic surface S ∈ ℂ2, and a given holomorphic function on S1 there exists a unique meromorphic solution of Burgers' equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg's iterative proof of the abstract Cauchy-Kowalevski theorem.

Blow-up of smooth solutions of the time-fractional Burgers equation

2019 ◽  
Vol 43 (2) ◽  
pp. 185-192 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Mokhtar Kirane ◽  
Berikbol T. Torebek
Keyword(s):  
Burgers Equation ◽  
Blow Up ◽  
Smooth Solutions

scholarly journals THE NON-VISCOUS BURGERS EQUATION ASSOCIATED WITH RANDOM POSITION IN COORDINATE SPACE: A THRESHOLD FOR BLOW UP BEHAVIOUR

2009 ◽  
Vol 19 (05) ◽  
pp. 749-767 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
OLGA ROZANOVA
Keyword(s):  
Burgers Equation ◽  
Blow Up ◽  
Critical Time ◽  
Threshold Effect ◽  
Critical Value ◽  
Initial Distribution ◽  
Coordinate Space ◽  
Random Position ◽  
The Mean ◽  
Particle Paths

It is well known that the solutions to the non-viscous Burgers equation develop a gradient catastrophe at a critical time provided the initial data have a negative derivative in certain points. We consider this equation assuming that the particle paths in the medium are governed by a random process with a variance which depends in a polynomial way on the velocity. Given an initial distribution of the particles which is uniform in space and with the initial velocity linearly depending on the position, we show both analytically and numerically that there exists a threshold effect: if the power in the above variance is less than 1, then the noise does not influence the solution behavior, in the following sense: the mean of the velocity when we keep the value of position fixed goes to infinity outside the origin. If, however, the power is larger or equal to 1, then this mean decays to zero as the time tends to a critical value.

scholarly journals Singularity Formation in the Inviscid Burgers Equation

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 848
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Lower Bound ◽  
Nonlinear Equation ◽  
Burgers Equation ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Singularity Formation ◽  
Priori Estimates ◽  
Inviscid Burgers Equation ◽  
Stability Type

We provide a lower bound for the blow up time of the H2 norm of the entropy solutions of the inviscid Burgers equation in terms of the H2 norm of the initial datum. This shows an interesting symmetry of the Burgers equation: the invariance of the space H2 under the action of such nonlinear equation. The argument is based on a priori estimates of energy and stability type for the (viscous) Burgers equation.

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