Conservation law of harmonic mappings in supercritical dimensions by Guo, Chang-Yu, Xiang, Chang-Lin

“…As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.…”
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Best practice mechanisms for biodiversity conservation law and policy by Callum Brockett, Katie Woolaston, Felicity Deane, Fran Humphries, Ethan Kumar, Amanda Kennedy, Justine Bell-James

“…We reviewed 128 publications from around the world to ascertain and synthesise best practices in law and policy that aim to protect and conserve biodiversity (herein termed ‘biodiversity conservation law’). The literature demonstrated that when it comes to biodiversity conservation law, the concept of ‘best practice’ is elusive, and does not necessarily equate to a reversal in species decline. …”
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On optimal regularity estimates for finite-entropy solutions of scalar conservation laws by Lamy, Xavier, Lorent, Andrew, Peng, Guanying

“…We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. …”
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Nonlinear asymptotic stability in $L^\infty $ for Lipschitz solutions to scalar conservation laws by Golding, William

“…In this note, we show nonlinear stability in $L^\infty $ for Lipschitz solutions to genuinely nonlinear, multi-dimensional scalar conservation laws. As an application, we are able to compute algebraic decay rates of the $L^\infty $ norm of perturbations of global-in-time Lipschitz solutions, including perturbations of planar rarefaction waves. …”
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Discontinuous nonlocal conservation laws and related discontinuous ODEs – Existence, Uniqueness, Stability and Regularity by Keimer, Alexander, Pflug, Lukas

“…We study nonlocal conservation laws with a discontinuous flux function of regularity $\mathsf {L}^{\infty }(\mathbb{R})$ in the spatial variable and show existence and uniqueness of weak solutions in $\mathsf {C}\big ([0,T]; \mathsf {L}^{1}_{\mathrm{loc}}\big )$, as well as related maximum principles. …”
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Analysis of the vacuum solution of the five-dimensional Einstein field equations with negative cosmological constant via variational symmetries by Fatemeh Ahangari

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A viscoelastic flow model of Maxwell-type with a symmetric-hyperbolic formulation by Boyaval, Sébastien

Subjects: “…Symmetric-hyperbolic systems of conservation laws…”
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Dynamical constraints on pseudo-gauge transformations by Zbigniew Drogosz, Wojciech Florkowski, Mykhailo Hontarenko, Radoslaw Ryblewski

“…For pseudo-gauge transformations connecting two symmetric energy-momentum tensors, we find that the super-potential Φλμν must obey a conservation law of the form ∂λΦλμν=0. This equation, referred to below as the STS condition, represents a constraint that is hardly possible to be satisfied for tensors constructed out of the basic hydrodynamic variables such as temperature, baryon chemical potential, and the hydrodynamic flow. …”
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Teaching ideal quantum measurement, from dynamics to interpretation by Allahverdyan, Armen E., Balian, Roger, Nieuwenhuizen, Theo M.

“…The resulting dynamical equations may be solved for simple models. Conservation laws are shown to entail two independent relaxation mechanisms: truncation and registration. …”
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Lie groups and continuum mechanics: where do we stand today? by de Saxcé, Géry, Razafindralandy, Dina

“…We consider the Lie symmetry group of the equations of a mechanical problem and investigate how to take advantage of them in developping analytical models (self-similar solutions, conservation laws, turbulence, ...) of the physical phenomena encoded in these equations. …”
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