Herbert Koch | Academic Influence

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Herbert Koch

Mathematics

#1191

World Rank

#1994

Historical Rank

Measure Theory

#3507

World Rank

#4137

Historical Rank

mathematics Degrees

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Mathematics

Herbert Koch's Degrees

PhD Mathematics University of Bonn

Why Is Herbert Koch Influential?

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According to Wikipedia, Herbert Koch is a German mathematician active in the field of partial differential equations. He occupies the position of a professor at the University of Bonn. Together with Daniel Tataru, he is known for his work on the well-posedness of the Navier–Stokes equations, one of their results being known as Koch–Tataru solution.

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Herbert Koch's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Well-posedness for the Navier–Stokes Equations (2001) (449)
Well-posedness and scattering for the KP-II equation in a critical space (2007) (252)
Dispersive estimates for principally normal pseudodifferential operators (2004) (200)
Carleman estimates and unique continuation for second-order elliptic equations with nonsmooth coefficients (2001) (163)
A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces (2006) (159)
Nonlinear wave interactions for the Benjamin-Ono equation. (2004) (150)
Geometric flows with rough initial data (2009) (147)
On the local well-posedness of the Benjamin-Ono equation in Hs(ℝ) (2003) (141)
A New Approach to Absolute Continuity of Elliptic Measure, with Applications to Non-symmetric Equations☆ (2000) (137)
L^p eigenfunction bounds for the Hermite operator (2004) (120)
Carleman Estimates and Absence of Embedded Eigenvalues (2005) (104)
Hadamard Well-posedness of Weak Solutions in Nonlinear Dynamic Elasticity-full von Karman Systems (2002) (86)
Renormalization of the two-dimensional stochastic nonlinear wave equations (2017) (77)
Dispersive Equations and Nonlinear Waves (2014) (71)
Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients (2007) (69)
Semiclassical Lp Estimates (2006) (62)
A Para-Differential Renormalization Technique for Nonlinear Dispersive Equations (2009) (58)
Higher regularity of the free boundary in the elliptic Signorini problem (2014) (57)
Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity (2018) (54)
Sharp counterexamples in unique continuation for second order elliptic equations (2002) (53)
Conserved energies for the cubic nonlinear Schrödinger equation in one dimension (2018) (49)
Energy and local energy bounds for the 1-d cubic NLS equation in H−14 (2010) (49)
DECAY OF MASS FOR A SEMILINEAR PARABOLIC EQUATION (1999) (47)
Spectral projections for the twisted Laplacian (2004) (47)
SEMICLASSICAL L p ESTIMATES (2014) (47)
Global existence of classical solutions to the dynamical von Kármán equations (1993) (45)
Erratum to “Well-posedness and scattering for the KP-II equation in a critical space” [Ann. I. H. Poincaré – AN 26 (3) (2009) 917–941] (2010) (43)
Transport and instability for perfect fluids (2002) (42)
On optimal regularity of free boundary problems and a conjecture of De Giorgi (2005) (41)
Dispersion Estimates for Third Order Equations in Two Dimensions (2003) (40)
Lp-Estimates for a Solution to the Nonstationary Stokes Equations (2001) (38)
Entropy of Eigenfunctions (2007) (36)
The Korteweg-de-Vries equation at H^{-1} regularity (2011) (36)
Global Dynamics for the Two-dimensional Stochastic Nonlinear Wave Equations (2020) (35)
Bounded compositions on scaling invariant Besov spaces (2012) (34)
Higher Regularity for the fractional thin obstacle problem (2016) (33)
Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps (2014) (33)
Slow decay in linear thermoelasticity (2000) (31)
Strong unique continuation for products of elliptic operators of second order (2009) (31)
Lq-Estimates of the First-Order Derivatives of Solutions to the Nonstationary Stokes Problem (2002) (28)
Small data scattering and soliton stability in Ḣ−1∕6 for the quartic KdV equation (2012) (26)
Mixed problems for fully nonlinear hyperbolic equations (1993) (26)
On finite energy solutions of the KP-I equation (2006) (26)
Uniqueness of the Modified Schrödinger Map in H 3/4+ϵ(ℝ2) (2007) (26)
On the spectrum of hyperbolic semigroups (1995) (24)
Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions (2002) (24)
Higher order time asymptotics of fast diffusion in euclidean space: a dynamical systems approach (2012) (22)
Self-similar solutions to super-critical gKdV (2014) (22)
Very singular solutions to a nonlinear parabolic equation with absorption II. Uniqueness (2001) (20)
The Variable Coefficient Thin Obstacle Problem: Optimal Regularity and Regularity of the Regular Free Boundary (2015) (19)
Conserved energies for the cubic NLS in 1-d (2016) (19)
An asymptotic sharp Sobolev regularity for planar infinity harmonic functions (2018) (19)
The Variable Coefficient Thin Obstacle Problem: Carleman Inequalities (2015) (18)
Flatness implies smoothness for solutions of the porous medium equation (2016) (18)
On center manifolds (1997) (17)
On instability mechanisms for inverse problems (2020) (16)
The Spectrum of a Hyperbolic Evolution Operator (1995) (15)
Local Smoothing and Local Solvability for Third Order Dispersive Equations (2007) (15)
Parabolic equations with rough data (2013) (13)
Stability and Hopf Bifurcation for Fully Nonlinear Parabolic-Hyperbolic Equations (2000) (13)
Convolution estimates for singular measures and some global nonlinear Brascamp—Lieb inequalities (2014) (12)
The variable coefficient thin obstacle problem: Higher regularity (2016) (11)
Recent Results on Unique Continuation for Second Order Elliptic Equations (2001) (9)
Doubling inequalities for the Lam\'e system with rough coefficients (2015) (9)
The cubic Szegő flow at low regularity (2016) (9)
Sharp $L^q$ bounds on spectral clusters for Holder metrics (2007) (7)
Global well-posedness and scattering for small data for the three-dimensional Kadomtsev–Petviashvili II equation (2017) (7)
Backward Uniqueness in Linear Thermoelasticity with Time and Space Variable Coefficients (2007) (7)
Partial differential equations with non-Euclidean geometries (2008) (6)
Partial analyticity and nodal sets for nonlinear elliptic systems (2015) (6)
Self-Sustained Oscillations of Nonlinearly Viscoelastic Layers (2000) (6)
Finite dimensional aspects of semilinear parabolic equations (1996) (5)
NONLINEAR DISPERSIVE EQUATIONS, SUMMER TERM 2013 (2013) (5)
Subcritical Lp bounds on spectral clusters for Lipschitz metrics (2007) (5)
Some sharp Sobolev regularity for inhomogeneous infinity Laplace equation in plane (2018) (5)
Boundary-degenerate Elliptic Operators and Hölder Continuity for Solutions to Variational Equations and Inequalities (2013) (5)
Multisolitons for the cubic NLS in 1-d and their stability (2020) (4)
Conserved energies for the one dimensional Gross-Pitaevskii equation (2018) (4)
Dispersive decay of small data solutions for the KdV equation (2019) (4)
On the spectral density function of the Laplacian of a graph (2012) (4)
Dirichlet problem for weakly harmonic maps with rough data (2021) (3)
Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin: “Fourier Analysis and Nonlinear Partial Differential Equations” (2014) (3)
Globak well-posedness and scattering for small data for the 3-d KP-II Cauchy problem (2016) (3)
Sharp Lp Bounds on Spectral Clusters for Lipschitz Metrics (2012) (2)
Functions of bounded p-variation (2014) (2)
Small data scattering and soliton stability in $\dot{H}^{-\frac16}$ for the quartic KdV Equation (2010) (2)
Adapted Function Spaces for Dispersive Equations (2014) (2)
Differentiability of Parabolic Semi-Flows in Lp-Spaces and Inertial Manifolds (2000) (1)
Uniqueness of the modified Schroedinger map in H^{3/4+e}(R^2) (2005) (1)
A multi-body system coupling wave equations in n and n − 1 space dimensions (2005) (1)
Pareto optimization of resonances and minimum-time control (2018) (1)
Convexity and concavity of the ground state energy (2015) (1)
Dispersive estimates and absence of embedded eigenvalues (2005) (1)
BOUNDS ON SPECTRAL CLUSTERS FOR HOLDER METRICS (2006) (1)
Long-time asymptotic expansions for nonlinear diffusions in Euclidean space ∗ (2014) (1)
Dispersive and Strichartz estimates (2014) (0)
Strichartz estimates and small data for the nonlinear Schrödinger equation (2014) (0)
Measurements of the rare decays $B \to K \ell^{+} \ell^{-}$ and $B \to K^{*} \ell^{+} \ell^{-}$ (2005) (0)
Mullen, Gary L., Peter Jau-Shyong Shiue (Eds.): Finite Fields, Coding Theory, and Advances in Communications and Computing. (Lecture Notes in Pure and Applied Mathematics, Volume 141) Marcel Dekker, Inc., New York, Basel, Hong Kong 1993, pp. 480, $145.00 (1994) (0)
An inverse Strichartz inequality (2014) (0)
Title Conserved energies for the cubic NLS in 1-d Permalink (0)
Global well-posedness and scattering for small data for the 2D and 3D KP-II Cauchy problem (2016) (0)
Appendix B: Bessel functions (2014) (0)
Van der Warden, B. L. A History of Algebra from al ‐ Khwarzmi to Emmy Noether. Springer‐Verlag, Berlin ‐ Heidelberg ‐ New York ‐ Tokyo 1985, VI, 271 S., 28 Abb., DM 98,‐ (2007) (0)
Higher regularity of the free boundary in a semilinear system (2022) (0)
Appendix A: Young’s inequality and interpolation (2014) (0)
Selfsimilar solution to supercritical gKdV (2014) (0)
A large data critical problem (2014) (0)
Concavity and convexity of the ground state energy (2015) (0)
Convolution of measures on hypersurfaces, bilinear estimates, and local smoothing (2014) (0)
Spectral projections for the twisted Laplacian by Herbert Koch ( Dortmund ) and (2007) (0)
Nonlinear Waves and Dispersive Equations (2023) (0)
Well-posedness for nonlinear dispersive equations (2014) (0)
LONG TIME ASYMPTOTICS FOR FAST DIFFUSION VIA DYNAMICAL SYSTEMS METHODS (2008) (0)
Ja n 20 04 DISPERSIVE ESTIMATES FOR PRINCIPALLY NORMAL PSEUDODIFFERENTIAL OPERATORS (2008) (0)
Existence of minimal blowup solutions and their properties (2014) (0)
A Palais–Smale type condition (2014) (0)
Maps into manifolds (2014) (0)
Bounds for KdV and the 1-d cubic NLS equation in rough function spaces (2011) (0)
Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin: “Fourier Analysis and Nonlinear Partial Differential Equations” (2013) (0)
Appendix A: Background material (2014) (0)
Index to Volume 136 2014 (2014) (0)
A linear profile decomposition (2014) (0)
Frequency-localized interaction Morawetz inequalities and applications (2014) (0)
TRANSPORT AND INSTABILITY FOR INCOMPRESSIBLE AND INVISCID FLUIDS (2007) (0)
Stationary phase and dispersive estimates (2014) (0)
Study of the decay B̅[superscript 0]→Λ[+ over c]p̅π[superscript +]π[superscript -] and its intermediate states (2013) (0)
Long-time Strichartz estimates and applications (2014) (0)
Stability theory for the energy-critical NLS (2014) (0)
Appendic C: The Fourier transform (2014) (0)

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