Stability of singular solutions to the Navier-Stokes system
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DOI: 10.1016/j.jde.2022.01.010
Abstract: We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem… read more here.
Keywords: solutions navier; navier stokes; stokes system; singular solutions ... See more keywords
Existence and uniqueness of singular solutions for a conservation law arising in magnetohydrodynamics
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DOI: 10.1088/1361-6544/aae04b
Abstract: The Brio system is a two-by-two system of conservation laws arising as a simplified model in ideal magnetohydrodynamics (MHD). The system has the form \begin{align*} \partial_t u+\partial_x \Big({\textstyle \frac{u^2+v^2}{2}}\Big)=0,\\ \partial_t v+\partial_x \big(v(u-1)\big)=0. \end{align*} It was… read more here.
Keywords: system; existence uniqueness; magnetohydrodynamics; conservation laws ... See more keywords
On singular solutions to Clairaut-type equations
Sign Up to like & getrecommendations! Published in 2019 at "Modern Physics Letters A"
DOI: 10.1142/s0217732319502584
Abstract: Singular solutions to the Clairaut-type equations in general setting when functions determined nonlinearity have a special form are studied. A number of new singular solutions are found. read more here.
Keywords: solutions clairaut; clairaut type; singular solutions; type equations ... See more keywords