Institutt for matematiske fag
Recent Submissions

Nonexistence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier–Stokes Equations
(Journal article; Peer reviewed, 2018)The wellposedness of classical solutions with finite energy to the compressible Navier–Stokes equations (CNS) subject to arbitrarily large and smooth initial data is a challenging problem. In the case when the fluid density ... 
Formation of singularities of spherically symmetric solutions to the 3D compressible Euler equations and Euler–Poisson equations
(Journal article; Peer reviewed, 2018)By introducing a new averaged quantity with a fast decay weight to perform Sideris's argument (Commun Math Phys, 1985) developed for the Euler Equations, we extend the formation of singularities of classical solution to ... 
Existence of a Highest Wave in a Fully Dispersive TwoWay Shallow Water Model
(Journal article; Peer reviewed, 2018)We consider the existence of periodic traveling waves in a bidirectional Whitham equation, combining the full twoway dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity. ... 
Smallamplitude fully localised solitary waves for the fulldispersion KadomtsevPetviashvili equation
(Journal article; Peer reviewed, 2018)The KPI equation arises as a weakly nonlinear model equation for gravitycapillary waves with strong surface tension (Bond number ). This equation admits—as an explicit solution—a 'fully localised' or 'lump' solitary ... 
Classical wellposedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces
(Journal article; Peer reviewed, 2018)For both localized and periodic initial data, we prove local existence in classical energy space Hs,s > 3 2 , for a class of dispersive equations ut +(n(u))x +Lux = 0 with nonlinearities of mild regularity. Our results are ... 
Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains
(Journal article; Peer reviewed, 2018)We prove that for a strongly pseudoconvex domain D ⊂ C n , the infinitesimal Carath´eodory metric gC (z, v) and the infinitesimal Kobayashi metric gK(z, v) coincide if z is sufficiently close to bD and if v is sufficiently ... 
Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
(Journal article; Peer reviewed, 2018)We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given real hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close ... 
Cone penetration data classification by Bayesian inversion with a Hidden Markov model
(Journal article; Peer reviewed, 2018)This study examines the application of the Hidden Markov model (HMM) to the soil classification based on Cone Penetration Test (CPT) measurements. The HMM is formulated in the Bayesian framework and composed of a Markov ... 
Spatial modelling with RINLA: A review
(Journal article; Peer reviewed, 2018)Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically‐sized datasets from scratch is ... 
Followtheleader models can be viewed as a numerical approximation to the LighthillWhithamRichards model for traffic flow
(Journal article; Peer reviewed, 2018) 
High pseudomoments of the Riemann zeta function
(Journal article, 2018)The pseudomoments of the Riemann zeta function, denoted Mk(N), are defined as the 2kth integral moments of the Nth partial sum of ζ(s) on the critical line. We improve the upper and lower bounds for the constants in the ... 
Symmetries and multipeakon solutions for the modified twocomponent CamassaHolm system
(Chapter, 2018)Compared with the twocomponent Camassa–Holm system, the modified twocomponent Camassa–Holm system introduces a regularized density which makes possible the existence of solutions of lower regularity, and in particular ... 
Existence and Lipschitz stability for αdissipative solutions of the twocomponent Hunter–Saxton system
(Journal article, 2018)We establish the concept of αdissipative solutions for the twocomponent Hunter–Saxton system under the assumption that either α(x)=1 or 0≤α(x)<1 for all x∈R. Furthermore, we investigate the Lipschitz stability of solutions ... 
Cohortwide deep whole genome sequencing and the allelic architecture of complex traits
(Journal article; Peer reviewed, 2018)The role of rare variants in complex traits remains uncharted. Here, we conduct deep whole genome sequencing of 1457 individuals from an isolated population, and test for rare variant burdens across six cardiometabolic ... 
On the Equivalence of Eulerian and Lagrangian Variables for the TwoComponent Camassa–Holm System
(Chapter, 2018)The Camassa–Holm equation and its twocomponent Camassa–Holm system generalization both experience wave breaking in finite time. To analyze this, and to obtain solutions past wave breaking, it is common to reformulate the ... 
Iteration of composition operators on small Bergman spaces of Dirichlet series
(Journal article; Peer reviewed, 2018)The Hilbert spaces Hw consisiting of Dirichlet series F(s) = P∞ n=1 an n −s that satisfty P∞ n=1 an 2 /wn < ∞, with {wn}n of average order logj n (the jfold logarithm of n), can be embedded into certain small Bergman ... 
Decomposition of Modules over finitedimensional Algebras
(Master thesis, 2018)We investigate algorithms for decomposing a module $M$ over a finitedimensional path algebra $\Lambda$. The algorithms first have to construct the endomorphism ring \[ \End(M) = \Hom(M, M). \] \noindent Consequently, ... 
Nonlinear TwoPoint Flux Approximation Schemes for Reservoir Simulation
(Master thesis, 2018)The main objective of this thesis has been to investigate some methods for simulating CO2 storage and hydrocarbon recovery on complex polyhedral grids, with main focus on the nonlinear twopoint flux approximation method. ... 
A General Nonlinear Reservoir Simulator with the Full Approximation Scheme
(Master thesis, 2018)Simulation of multiphase flow and transport in porous rock formations gives rise to large systems of strongly coupled nonlinear equations. Solving these equations is computationally challenging because of orders of magnitude ... 
Multilevel Analysis Applied to Fetal Growth Data with Missing Values.
(Master thesis, 2006)Intrauterine growth retardation means that the growth of a fetus is restricted as compared with its biological growth potential. This contributes to an increased risk for illnesses or death of the newborn. Therefore it ...