
Hierarchical construction of bounded solutions in critical regularity spaces CPAM, to appear.

Critical thresholds in 1D Euler equations with nonlocal forces (with J. A. Carrillo, Y.P. Choi and C. Tan), http://arxiv.org/abs/1411.1791

Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws
(with U. Fjordholm, R, Kappeli and S. Mishra),
preprint

Heterophilious dynamics enhances consensus (with S. Motsch), SIAM Review 56(4) (2014) 577–621 (with Introduction by D. J. Higham)

Stability and spectral convergence of Fourier method for nonlinear problems. On the shortcomings of the 2/3 dealiasing method (with C. Bardos),
Numerische Mathematik (2014).

Critical thresholds in flocking hydrodynamics with nonlocal alignment (with C. Tan),
Proc. Royal Soc. A 372:20130401 (2014).

Dissipation vs. quadratic nonlinearity: from a priori energy bound to higherorder regularizing effect (with A. Biswas),
Nonlinearity 27 (2014) 545562.

A review of numerical methods for nonlinear partial differential equations, Bull. AMS 49(4) (2012) 507554.

ENO reconstruction and ENO interpolation are stable (with U. Fjordholm & S. Mishra), FoCM 13(2) (2012) 139159.

A new model for selforganized dynamics and its flocking behavior (with S. Motsch), J. Stat. Physics 144(5) (2011) 923947.

Hierarchical construction of bounded solutions of div U=F in critical regularity spaces (with C. Tan)
``Nonlinear Partial Differential Equations'', Proc. 2010 Abel Symposium (H. Holden & K. Karlsen eds.), Abel Symposia 7, Springer (2011), pp. 255269.

Wellbalanced and energy stable schemes for the shallow water equations with discontinuous topography (with U. Fjordholm & S. Mishra)
J. Computational Physics 230 (2011), 55875609.
 Integrodifferential equations based on (BV, L^{1}) image decomposition (with P. Athavale)
SIAM J. Imaging Sciences 4(1) (2011) 300312.

Global regularity of the 4D Restricted Euler Equations (with H. Liu & D. Wei)
Physica D 239 (2010) 12251231.
 Constraint preserving schemes using potentialbased fluxes (with S. Mishra)
I.
Multidimensional transport equations Comm. Comput. Phys. 9(3) (2010) 688710.
II.
Genuinely multidimensional systems of conservation laws. SINUM 49(3) (2011) 10231045. III.
Genuinely multidimensional schemes for the MHD equations
M2AN 46 (2012) 661680.

Hyperbolic Problems: Theory, Numerics, Applications Proceedings of HYP2008, Univ. of Maryland, College Park, June 913, 2008
AMS Proc. Symp. Appl. Math., 2009 (with J.G. Liu & A. Tzavaras) Vol. 67.1: Plenary & Invited Talks; Vol. 67.2: Contributed Talks.

Energypreserving and stable approximations for the twodimensional shallow water equations (with W. Zhong)
in "Mathematics and Computation  A Contemporary View", Proc. of the Third Abel Symposium (H. MuntheKaas & B. Owren eds.), Springer 2008, pp. 6794.

From particle to kinetic and hydrodynamic descriptions of flocking (with S.Y. Ha)
Kinetic and Related Models 1(3) (2008) 415435.

L^{2}stability analysis of the central Discontinuous Galerkin method and a comparison between the central and regular
Discontinuous Galerkin methods
(with Y.J. Liu, C.W. Shu & M. Zhang) M2AN 42 (2008) 593607
[highlighted paper].

Multiscale hierarchical decomposition of images with applications to deblurring, denoising and segmentation
(with S. Nezzar & L. Vese) Comm. Math. Sciences 6(2) (2008) 281307.

Recovery of edges from spectral data with noisea new perspective (with S. Engelberg)
SINUM 46(5) (2008), 26202635.

Long time existence of smooth solutions for the rapidly rotating shallowwater and
Euler equations (with B. Cheng)
SIAM J. Math. Anal. 39(5) (2008) 16681685.

Filters, mollifiers and the computation of the Gibbs phenomenon
Acta Numerica 16 (2007) 305378.
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Velocity averaging, kinetic formulations and regularizing effects in quasilinear PDEs (with T. Tao)
CPAM 60 (2007), 14881521.
 Entropy
stability theory for difference approximations of nonlinear
conservation laws and related time dependent problems
Acta Numerica 12 (2003), 451512.
 Hyperbolic
Problems: Theory, Numerics, Applications Proceedings of the
Ninth International Conference on Hyperbolic Problems held in
CalTech, Pasadena, March 2529, 2002 (with T. Hou),
SpringerVerlag, ISBN: 3540443339, 2003. Table of
content
 High
resolution methods for time dependent problems with piecewise
smooth solutions "International Congress of
Mathematicians", Proceedings of the ICM02 Beijing 2002 (Li
Tatsien, ed.), Vol. III: Invited lectures, Higher Education
Press (2002) 747757.
 On
a new scale of regularity spaces with applications to Euler's
equations Nonlinearity 14 (2001) 513532.

Strong stabilitypreserving
highorder time discretization methods (with S. Gottlieb & C.W. Shu) SIAM Review
43 (2001) 89112.
 New
high resolution central schemes for nonlinear conservation laws
and convectiondiffusion equations (with A. Kurganov)
JCP, 160 (2000) 241282.
 Approximate
solutions of the incompressible Euler equations with no
concentrations (with M. Lopes Filho & H. J. Nussenzveig)
Annal. De L'institut Henri Poincare (c) Non Linear
Analysis, 17 (2000) 371412.
 Approximate
solution of nonlinear conservation laws and related equations
"Recent Advances in Partial Differential Equations and
Applications" 1996 Venice Conference R. Spigler and S. Venakides
eds.), AMS Proc. Symp. Appl. Math. 54 (1998) 325368.
 A
kinetic formulation of multidimensional scalar conservation laws
and related equations (with P.L. Lions & B. Perthame)
J. Amer. Math. Soc. 7 (1994) 169191.
 Local
error estimates for discontinuous solutions of nonlinear
hyperbolic equations SINUM 28 (1991) 891906.
 A
kinetic equation with kinetic entropy functions for scalar
conservation Laws (with B. Perthame) Comm. Math. Phys.
136 (1991) 501517.
 Nonoscillatory
central differencing for hyperbolic conservation laws (with H.
Nessyahu) JCP 87 (1990) 408463.
 An
O(N^{2}) method for computing the eigensystem of N x N
symmetric tridiagonal matrices by the divide and conquer
approach (with D. Gill) SIAM J. Scientific Computing 11 (1990) 161173.
 Convergence
of spectral methods for nonlinear conservation laws
SINUM 26 (1989) 3044.
 Numerical
viscosity and the entropy condition for conservative difference
schemes Math. Comp. 43 (1984) 369381
 The
equivalence of L^{2}stability, the resolvent condition
and strict Hstability LAA 41 (1981)
151159.
 Schemeindependent
stability criteria for difference approximations of hyperbolic
initialboundary value problems. II (with M. Goldberg)
Math. Comp. 36 (1981) 603626.
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