Helge Kristian Jenssen
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View article: Non-isentropic cavity flow for the multi-d compressible Euler system
Non-isentropic cavity flow for the multi-d compressible Euler system Open
We rigorously construct non-isentropic and self-similar multi-d Euler flows in which a central cavity (vacuum region) collapses. While isentropic flows of this type have been analyzed earlier by Hunter \cite{hun_60} and others, the non-ise…
View article: Amplitude blowup in compressible Euler flows without shock formation
Amplitude blowup in compressible Euler flows without shock formation Open
Recent works have demonstrated that continuous self-similar radial Euler flows can drive primary (non-differentiated) flow variables to infinity at the center of motion. Among the variables that blow up at collapse is the pressure, and it …
View article: Gradient blowup without shock formation in compressible Euler flow
Gradient blowup without shock formation in compressible Euler flow Open
The well-known Guderley similarity solution provides a fundamental example of how a spherically converging shock wave can generate amplitude blowup in compressible Euler flow. Recent work has shown that the same phenomenon can occur in con…
View article: 1-D Isentropic Euler flows: Self-similar Vacuum Solutions
1-D Isentropic Euler flows: Self-similar Vacuum Solutions Open
We consider one-dimensional self-similar solutions to the isentropic Euler system when the initial data are at vacuum to the left of the origin. For $x>0$ the initial velocity and sound speed are of form $u_0(x)=u_+x^{1-λ}$ and $c_0(x)=c_+…
View article: Extensions of BV compactness criteria
Extensions of BV compactness criteria Open
Helly's selection theorem provides a criterion for compactness of sets of single-variable functions with bounded pointwise variation. Fra{ň}kov{á} has given a proper extension of Helly's theorem to the setting of single-variable regulated …
View article: Radially Symmetric Non-isentropic Euler flows: continuous blowup with positive pressure
Radially Symmetric Non-isentropic Euler flows: continuous blowup with positive pressure Open
Guderley's 1942 work on radial shock waves provides cases of self-similar Euler flows exhibiting blowup of primary (undifferentiated) flow variables: a converging shock wave invades a quiescent region, and the velocity and pressure in its …
View article: Variation Instability Near Vacuum in One-Dimensional Isentropic Flow
Variation Instability Near Vacuum in One-Dimensional Isentropic Flow Open
We consider instability of the total variation in shock-only solutions to the one-dimensional isentropic Euler system. The main results concern the possibility of immediate blowup in variation of the density field $\rho $ when the data app…
View article: New Self-similar Euler Flows: gradient catastrophe without shock formation
New Self-similar Euler Flows: gradient catastrophe without shock formation Open
We consider self-similar solutions to the full compressible Euler system for an ideal gas in two and three space dimensions. The system admits a 2-parameter family of similarity solutions depending on parameters $λ$ and $κ$. Requiring loca…
View article: On BV-instability and existence for linearized radial Euler flows
On BV-instability and existence for linearized radial Euler flows Open
We provide concrete examples of immediate BV-blowup from small and radially symmetric initial data for the 3-dimensional, linearized Euler system. More precisely, we exhibit data arbitrarily close to a constant state, measured in L-infinit…
View article: FINN.no Slates Dataset: A new Sequential Dataset Logging Interactions, all Viewed Items and Click Responses/No-Click for Recommender Systems Research
FINN.no Slates Dataset: A new Sequential Dataset Logging Interactions, all Viewed Items and Click Responses/No-Click for Recommender Systems Research Open
We present a novel recommender systems dataset that records the sequential interactions between users and an online marketplace. The users are sequentially presented with both recommendations and search results in the form of ranked lists …
View article: Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion
Equivalence of low frequency stability conditions for multidimensional detonations in three models of combustion Open
We use the classical normal mode approach of hydrodynamic stability theory to define stability determinants (Evans functions) for multidimensional strong detonations in three commonly studied models of combustion: the full reactive Navier-…
View article: Singularly perturbed ODEs and profiles for stationary symmetric Euler and Navier-Stokes shocks
Singularly perturbed ODEs and profiles for stationary symmetric Euler and Navier-Stokes shocks Open
We construct stationary solutions to the non-barotropic, compressible Euler and Navier-Stokes equations in several space dimensions with spherical or cylindrical symmetry. The equation of state is assumed to satisfy standard monotonicity a…
View article: Symmetric Euler and Navier–Stokes shocks in stationary barotropic flow on a bounded domain
Symmetric Euler and Navier–Stokes shocks in stationary barotropic flow on a bounded domain Open
We construct stationary solutions to the barotropic, compressible Euler and Navier–Stokes equations in several space dimensions with spherical or cylindrical symmetry. For given Dirichlet data on a sphere or a cylinder we first construct s…
View article: On Φ-variation for 1-d scalar conservation laws
On Φ-variation for 1-d scalar conservation laws Open
Let [Formula: see text] be a convex function satisfying [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text]. Consider the unique entropy admissible (i.e. Kružkov) solution [Formula: see text] of the sc…
View article: A mixed boundary value problem for $u_{xy}=f(x,y,u,u_x,u_y)$
A mixed boundary value problem for $u_{xy}=f(x,y,u,u_x,u_y)$ Open
Consider a single hyperbolic PDE $u_{xy}=f(x,y,u,u_x,u_y)$, with locally prescribed data: $u$ along a non-characteristic curve $M$ and $u_x$ along a non-characteristic curve $N$. We assume that $M$ and $N$ are graphs of one-to-one function…
View article: On similarity flows for the compressible Euler system
On similarity flows for the compressible Euler system Open
Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows, t…
View article: On Two Theorems of Darboux
On Two Theorems of Darboux Open
We provide precise formulations and proofs of two theorems from Darboux's lectures on orthogonal systems. These results provide local existence and uniqueness of solutions to certain types of first order PDE systems where each equation con…
View article: Convergence of exterior solutions to radial Cauchy solutions for $\partial_t^2U-c^2\Delta U=0$
Convergence of exterior solutions to radial Cauchy solutions for $\partial_t^2U-c^2\Delta U=0$ Open
Consider the Cauchy problem for the 3-D linear wave equation $\partial_t^2U-c^2\Delta U=0$ with radial initial data $U(0,x)=\Phi(x)=\varphi(|x|)$, $U_t(0,x)=\Psi(x)=\psi(|x|)$. A standard result states that $U$ belongs to $C([0,T];H^s(\mat…
View article: On convergence of exterior solutions to radial Cauchy solutions for $\square_{1+3}U=0$
On convergence of exterior solutions to radial Cauchy solutions for $\square_{1+3}U=0$ Open
Consider the Cauchy problem for the 3-d linear wave equation $\square_{1+3}U=0$ with radial initial data $U(0,x)=Φ(x)=ϕ(|x|)$, $U_t(0,x)=Ψ(x)=ψ(|x|)$. A standard result gives that $U$ belongs to $C([0,T];H^s(\mathbb{R}^3))$ whenever $(Φ,Ψ)…