TY - JOUR

T1 - Stability of a supersonic flow past a wedge with adjoint weak neutrally stable shock wave

AU - Blokhin, A. M.

AU - Tkachev, D. L.

PY - 2017/4/1

Y1 - 2017/4/1

N2 - We study the classical problem of a supersonic stationary flow of a nonviscous nonheat-conducting gas in local thermodynamic equilibrium past an infinite plane wedge. Under the Lopatinskiĭ condition on the shock wave (neutral stability), we prove the well-posedness of the linearized mixed problem (the main solution is a weak shock wave), obtain a representation of the classical solution, where, in this case (in contrast to the case of the uniform Lopatinskiĭ condition—an absolutely stable shock wave), plane waves additionally appear in the representation. If the initial data have compact support, the solution reaches the given regime in infinite time.

AB - We study the classical problem of a supersonic stationary flow of a nonviscous nonheat-conducting gas in local thermodynamic equilibrium past an infinite plane wedge. Under the Lopatinskiĭ condition on the shock wave (neutral stability), we prove the well-posedness of the linearized mixed problem (the main solution is a weak shock wave), obtain a representation of the classical solution, where, in this case (in contrast to the case of the uniform Lopatinskiĭ condition—an absolutely stable shock wave), plane waves additionally appear in the representation. If the initial data have compact support, the solution reaches the given regime in infinite time.

KW - (Lyapunov) asymptotic stability

KW - Lopatinskiĭ condition

KW - weak shock wave

UR - http://www.scopus.com/inward/record.url?scp=85020042331&partnerID=8YFLogxK

U2 - 10.3103/S1055134417020018

DO - 10.3103/S1055134417020018

M3 - Article

AN - SCOPUS:85020042331

VL - 27

SP - 77

EP - 102

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 2

ER -