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,
arxiv:1601.01937.
Preprint. 8) A.Boritchev, Decaying convergence for the fractional subcritical Burgers equation, accepted to Discrete and Continuous Dynamical Systems,
arxiv:1608.01460.
Preprint. 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. |