Papers and Preprints

Articles and preprints:

1) A.Boritchev, Estimates for Solutions of a Low-Viscosity Kick-Forced Generalised Burgers Equation, Proceedings of the Royal Society of Edinburgh A, 143(2), 2013, 253-268.
Preprint.
Final version.

2) A.Boritchev, K.Khanin, On Hyperbolicity of Minimizers for 1D Random Lagrangian systems, Nonlinearity, 26, 1 (2013), 65-80.
Preprint.
Final version.

3) A.Boritchev, Sharp Estimates for Turbulence in White-Forced Generalised Burgers Equation, Geometric and Functional Analysis, 23 (2013), 6, 1730-1771.
Preprint.
Final version.

4) A.Boritchev, Decaying Turbulence in a Generalised Burgers Equation, Archive for Rational Mechanics and Analysis, 214 (2014), 1, 331-357.
Preprint.
Final version.

5) A.Boritchev, Turbulence for the generalised Burgers Equation (review article), Russian Mathematical Surveys, 69:6(2014), 957-994.
Preprint.
Final version.

6) A.Boritchev, Multidimensional potential Burgers turbulence, Communications in Mathematical Physics, 2016, 342:441.
Preprint.
Final version.
Erratum, Communications in Mathematical Physics, 2016, 344:369.
Preprint.
Final version.

7) A.Boritchev, Exponential convergence to the stationary measure for a class of 1D Lagrangian systems with random forcing, Stochastic and Partial Differential Equations : Analysis and Computation, 2018, 6 : 109-123.
Preprint.
Final version.

8) A.Boritchev, Decaying convergence for the fractional subcritical Burgers equation, Discrete and Continuous Dynamical Systems A, 2018, 38(5) : 2229-2249.
Preprint.
Final version.


Proceedings:

1) A.Boritchev, 1D Burgers Turbulence: a model case for the Kolmogorov theory (in French), Laurent Schwartz seminar - PDE and applications (2011-2012), Exp. No. 40,
Preprint.
Final version.

Ph.D. thesis:

Defended on October 8, 2012 at Ecole Polytechnique: Generalised Burgers equation with random force and small viscosity.
Text of the thesis.
Slides shown at the Ph.D. defense.